# Question derivations [Previous](https://ocme.evemisslab.com/en/questions/page/97/) Page 98 / 180 [Next](https://ocme.evemisslab.com/en/questions/page/99/) All 36000 derivations have bilingual display, basic symbol and structural checks, and questions 1–36000 all have second-context mathematical and bilingual review; no display/symbol-checked candidates remain. This cohort has 36000 questions. 36000 derivations are published: 36000 mathematically reviewed and 0 display/symbol-checked candidates. 0 are not published here. - [Question 19401: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0051/) · R0037-19401 · Mathematically reviewed - [Question 19402: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0052/) · R0037-19402 · Mathematically reviewed - [Question 19403: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0053/) · R0037-19403 · Mathematically reviewed - [Question 19404: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0054/) · R0037-19404 · Mathematically reviewed - [Question 19405: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0055/) · R0037-19405 · Mathematically reviewed - [Question 19406: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0056/) · R0037-19406 · Mathematically reviewed - [Question 19407: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0057/) · R0037-19407 · Mathematically reviewed - [Question 19408: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0058/) · R0037-19408 · Mathematically reviewed - [Question 19409: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0059/) · R0037-19409 · Mathematically reviewed - [Question 19410: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0060/) · R0037-19410 · Mathematically reviewed - [Question 19411: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0061/) · R0037-19411 · Mathematically reviewed - [Question 19412: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0062/) · R0037-19412 · Mathematically reviewed - [Question 19413: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0063/) · R0037-19413 · Mathematically reviewed - [Question 19414: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0064/) · R0037-19414 · Mathematically reviewed - [Question 19415: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0065/) · R0037-19415 · Mathematically reviewed - [Question 19416: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0066/) · R0037-19416 · Mathematically reviewed - [Question 19417: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0067/) · R0037-19417 · Mathematically reviewed - [Question 19418: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0068/) · R0037-19418 · Mathematically reviewed - [Question 19419: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0069/) · R0037-19419 · Mathematically reviewed - [Question 19420: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0070/) · R0037-19420 · Mathematically reviewed - [Question 19421: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0071/) · R0037-19421 · Mathematically reviewed - [Question 19422: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0072/) · R0037-19422 · Mathematically reviewed - [Question 19423: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0073/) · R0037-19423 · Mathematically reviewed - [Question 19424: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0074/) · R0037-19424 · Mathematically reviewed - [Question 19425: Exact Chromatic Number Needs Both Lower and Upper Evidence](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0075/) · R0037-19425 · Mathematically reviewed - [Question 19426: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0076/) · R0037-19426 · Mathematically reviewed - [Question 19427: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0077/) · R0037-19427 · Mathematically reviewed - [Question 19428: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0078/) · R0037-19428 · Mathematically reviewed - [Question 19429: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0079/) · R0037-19429 · Mathematically reviewed - [Question 19430: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0080/) · R0037-19430 · Mathematically reviewed - [Question 19431: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0081/) · R0037-19431 · Mathematically reviewed - [Question 19432: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0082/) · R0037-19432 · Mathematically reviewed - [Question 19433: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0083/) · R0037-19433 · Mathematically reviewed - [Question 19434: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0084/) · R0037-19434 · Mathematically reviewed - [Question 19435: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0085/) · R0037-19435 · Mathematically reviewed - [Question 19436: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0086/) · R0037-19436 · Mathematically reviewed - [Question 19437: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0087/) · R0037-19437 · Mathematically reviewed - [Question 19438: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0088/) · R0037-19438 · Mathematically reviewed - [Question 19439: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0089/) · R0037-19439 · Mathematically reviewed - [Question 19440: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0090/) · R0037-19440 · Mathematically reviewed - [Question 19441: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0091/) · R0037-19441 · Mathematically reviewed - [Question 19442: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0092/) · R0037-19442 · Mathematically reviewed - [Question 19443: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0093/) · R0037-19443 · Mathematically reviewed - [Question 19444: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0094/) · R0037-19444 · Mathematically reviewed - [Question 19445: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0095/) · R0037-19445 · Mathematically reviewed - [Question 19446: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0096/) · R0037-19446 · Mathematically reviewed - [Question 19447: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0097/) · R0037-19447 · Mathematically reviewed - [Question 19448: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0098/) · R0037-19448 · Mathematically reviewed - [Question 19449: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0099/) · R0037-19449 · Mathematically reviewed - [Question 19450: Equality of k with the Minimum Is Not Validity of This Coloring](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0100/) · R0037-19450 · Mathematically reviewed - [Question 19451: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0001/) · R0037-19451 · Mathematically reviewed - [Question 19452: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0002/) · R0037-19452 · Mathematically reviewed - [Question 19453: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0003/) · R0037-19453 · Mathematically reviewed - [Question 19454: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0004/) · R0037-19454 · Mathematically reviewed - [Question 19455: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0005/) · R0037-19455 · Mathematically reviewed - [Question 19456: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0006/) · R0037-19456 · Mathematically reviewed - [Question 19457: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0007/) · R0037-19457 · Mathematically reviewed - [Question 19458: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0008/) · R0037-19458 · Mathematically reviewed - [Question 19459: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0009/) · R0037-19459 · Mathematically reviewed - [Question 19460: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0010/) · R0037-19460 · Mathematically reviewed - [Question 19461: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0011/) · R0037-19461 · Mathematically reviewed - [Question 19462: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0012/) · R0037-19462 · Mathematically reviewed - [Question 19463: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0013/) · R0037-19463 · Mathematically reviewed - [Question 19464: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0014/) · R0037-19464 · Mathematically reviewed - [Question 19465: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0015/) · R0037-19465 · Mathematically reviewed - [Question 19466: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0016/) · R0037-19466 · Mathematically reviewed - [Question 19467: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0017/) · R0037-19467 · Mathematically reviewed - [Question 19468: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0018/) · R0037-19468 · Mathematically reviewed - [Question 19469: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0019/) · R0037-19469 · Mathematically reviewed - [Question 19470: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0020/) · R0037-19470 · Mathematically reviewed - [Question 19471: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0021/) · R0037-19471 · Mathematically reviewed - [Question 19472: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0022/) · R0037-19472 · Mathematically reviewed - [Question 19473: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0023/) · R0037-19473 · Mathematically reviewed - [Question 19474: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0024/) · R0037-19474 · Mathematically reviewed - [Question 19475: Proper Coloring Alone Does Not Prove the Chromatic Minimum](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0025/) · R0037-19475 · Mathematically reviewed - [Question 19476: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0026/) · R0037-19476 · Mathematically reviewed - [Question 19477: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0027/) · R0037-19477 · Mathematically reviewed - [Question 19478: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0028/) · R0037-19478 · Mathematically reviewed - [Question 19479: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0029/) · R0037-19479 · Mathematically reviewed - [Question 19480: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0030/) · R0037-19480 · Mathematically reviewed - [Question 19481: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0031/) · R0037-19481 · Mathematically reviewed - [Question 19482: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0032/) · R0037-19482 · Mathematically reviewed - [Question 19483: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0033/) · R0037-19483 · Mathematically reviewed - [Question 19484: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0034/) · R0037-19484 · Mathematically reviewed - [Question 19485: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0035/) · R0037-19485 · Mathematically reviewed - [Question 19486: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0036/) · R0037-19486 · Mathematically reviewed - [Question 19487: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0037/) · R0037-19487 · Mathematically reviewed - [Question 19488: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0038/) · R0037-19488 · Mathematically reviewed - [Question 19489: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0039/) · R0037-19489 · Mathematically reviewed - [Question 19490: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0040/) · R0037-19490 · Mathematically reviewed - [Question 19491: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0041/) · R0037-19491 · Mathematically reviewed - [Question 19492: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0042/) · R0037-19492 · Mathematically reviewed - [Question 19493: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0043/) · R0037-19493 · Mathematically reviewed - [Question 19494: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0044/) · R0037-19494 · Mathematically reviewed - [Question 19495: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0045/) · R0037-19495 · Mathematically reviewed - [Question 19496: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0046/) · R0037-19496 · Mathematically reviewed - [Question 19497: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0047/) · R0037-19497 · Mathematically reviewed - [Question 19498: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0048/) · R0037-19498 · Mathematically reviewed - [Question 19499: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0049/) · R0037-19499 · Mathematically reviewed - [Question 19500: A Supplied k-Palette Is a Candidate Upper Certificate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0050/) · R0037-19500 · Mathematically reviewed - [Question 19501: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0001/) · R0038-19501 · Mathematically reviewed - [Question 19502: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0002/) · R0038-19502 · Mathematically reviewed - [Question 19503: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0003/) · R0038-19503 · Mathematically reviewed - [Question 19504: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0004/) · R0038-19504 · Mathematically reviewed - [Question 19505: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0005/) · R0038-19505 · Mathematically reviewed - [Question 19506: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0006/) · R0038-19506 · Mathematically reviewed - [Question 19507: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0007/) · R0038-19507 · Mathematically reviewed - [Question 19508: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0008/) · R0038-19508 · Mathematically reviewed - [Question 19509: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0009/) · R0038-19509 · Mathematically reviewed - [Question 19510: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0010/) · R0038-19510 · Mathematically reviewed - [Question 19511: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0011/) · R0038-19511 · Mathematically reviewed - [Question 19512: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0012/) · R0038-19512 · Mathematically reviewed - [Question 19513: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0013/) · R0038-19513 · Mathematically reviewed - [Question 19514: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0014/) · R0038-19514 · Mathematically reviewed - [Question 19515: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0015/) · R0038-19515 · Mathematically reviewed - [Question 19516: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0016/) · R0038-19516 · Mathematically reviewed - [Question 19517: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0017/) · R0038-19517 · Mathematically reviewed - [Question 19518: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0018/) · R0038-19518 · Mathematically reviewed - [Question 19519: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0019/) · R0038-19519 · Mathematically reviewed - [Question 19520: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0020/) · R0038-19520 · Mathematically reviewed - [Question 19521: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0021/) · R0038-19521 · Mathematically reviewed - [Question 19522: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0022/) · R0038-19522 · Mathematically reviewed - [Question 19523: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0023/) · R0038-19523 · Mathematically reviewed - [Question 19524: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0024/) · R0038-19524 · Mathematically reviewed - [Question 19525: Only a Valid Clique Size Certifies a Clique-Number Lower Bound](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0025/) · R0038-19525 · Mathematically reviewed - [Question 19526: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0051/) · R0038-19526 · Mathematically reviewed - [Question 19527: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0052/) · R0038-19527 · Mathematically reviewed - [Question 19528: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0053/) · R0038-19528 · Mathematically reviewed - [Question 19529: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0054/) · R0038-19529 · Mathematically reviewed - [Question 19530: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0055/) · R0038-19530 · Mathematically reviewed - [Question 19531: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0056/) · R0038-19531 · Mathematically reviewed - [Question 19532: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0057/) · R0038-19532 · Mathematically reviewed - [Question 19533: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0058/) · R0038-19533 · Mathematically reviewed - [Question 19534: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0059/) · R0038-19534 · Mathematically reviewed - [Question 19535: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0060/) · R0038-19535 · Mathematically reviewed - [Question 19536: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0061/) · R0038-19536 · Mathematically reviewed - [Question 19537: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0062/) · R0038-19537 · Mathematically reviewed - [Question 19538: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0063/) · R0038-19538 · Mathematically reviewed - [Question 19539: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0064/) · R0038-19539 · Mathematically reviewed - [Question 19540: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0065/) · R0038-19540 · Mathematically reviewed - [Question 19541: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0066/) · R0038-19541 · Mathematically reviewed - [Question 19542: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0067/) · R0038-19542 · Mathematically reviewed - [Question 19543: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0068/) · R0038-19543 · Mathematically reviewed - [Question 19544: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0069/) · R0038-19544 · Mathematically reviewed - [Question 19545: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0070/) · R0038-19545 · Mathematically reviewed - [Question 19546: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0071/) · R0038-19546 · Mathematically reviewed - [Question 19547: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0072/) · R0038-19547 · Mathematically reviewed - [Question 19548: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0073/) · R0038-19548 · Mathematically reviewed - [Question 19549: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0074/) · R0038-19549 · Mathematically reviewed - [Question 19550: Exact Extremal Sizes Need the Complete Vertex-Subset Search](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0075/) · R0038-19550 · Mathematically reviewed - [Question 19551: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0026/) · R0038-19551 · Mathematically reviewed - [Question 19552: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0027/) · R0038-19552 · Mathematically reviewed - [Question 19553: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0028/) · R0038-19553 · Mathematically reviewed - [Question 19554: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0029/) · R0038-19554 · Mathematically reviewed - [Question 19555: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0030/) · R0038-19555 · Mathematically reviewed - [Question 19556: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0031/) · R0038-19556 · Mathematically reviewed - [Question 19557: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0032/) · R0038-19557 · Mathematically reviewed - [Question 19558: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0033/) · R0038-19558 · Mathematically reviewed - [Question 19559: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0034/) · R0038-19559 · Mathematically reviewed - [Question 19560: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0035/) · R0038-19560 · Mathematically reviewed - [Question 19561: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0036/) · R0038-19561 · Mathematically reviewed - [Question 19562: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0037/) · R0038-19562 · Mathematically reviewed - [Question 19563: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0038/) · R0038-19563 · Mathematically reviewed - [Question 19564: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0039/) · R0038-19564 · Mathematically reviewed - [Question 19565: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0040/) · R0038-19565 · Mathematically reviewed - [Question 19566: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0041/) · R0038-19566 · Mathematically reviewed - [Question 19567: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0042/) · R0038-19567 · Mathematically reviewed - [Question 19568: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0043/) · R0038-19568 · Mathematically reviewed - [Question 19569: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0044/) · R0038-19569 · Mathematically reviewed - [Question 19570: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0045/) · R0038-19570 · Mathematically reviewed - [Question 19571: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0046/) · R0038-19571 · Mathematically reviewed - [Question 19572: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0047/) · R0038-19572 · Mathematically reviewed - [Question 19573: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0048/) · R0038-19573 · Mathematically reviewed - [Question 19574: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0049/) · R0038-19574 · Mathematically reviewed - [Question 19575: An Independent Set Is a Clique in the Complement](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0050/) · R0038-19575 · Mathematically reviewed - [Question 19576: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0076/) · R0038-19576 · Mathematically reviewed - [Question 19577: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0077/) · R0038-19577 · Mathematically reviewed - [Question 19578: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0078/) · R0038-19578 · Mathematically reviewed - [Question 19579: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0079/) · R0038-19579 · Mathematically reviewed - [Question 19580: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0080/) · R0038-19580 · Mathematically reviewed - [Question 19581: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0081/) · R0038-19581 · Mathematically reviewed - [Question 19582: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0082/) · R0038-19582 · Mathematically reviewed - [Question 19583: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0083/) · R0038-19583 · Mathematically reviewed - [Question 19584: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0084/) · R0038-19584 · Mathematically reviewed - [Question 19585: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0085/) · R0038-19585 · Mathematically reviewed - [Question 19586: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0086/) · R0038-19586 · Mathematically reviewed - [Question 19587: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0087/) · R0038-19587 · Mathematically reviewed - [Question 19588: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0088/) · R0038-19588 · Mathematically reviewed - [Question 19589: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0089/) · R0038-19589 · Mathematically reviewed - [Question 19590: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0090/) · R0038-19590 · Mathematically reviewed - [Question 19591: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0091/) · R0038-19591 · Mathematically reviewed - [Question 19592: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0092/) · R0038-19592 · Mathematically reviewed - [Question 19593: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0093/) · R0038-19593 · Mathematically reviewed - [Question 19594: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0094/) · R0038-19594 · Mathematically reviewed - [Question 19595: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0095/) · R0038-19595 · Mathematically reviewed - [Question 19596: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0096/) · R0038-19596 · Mathematically reviewed - [Question 19597: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0097/) · R0038-19597 · Mathematically reviewed - [Question 19598: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0098/) · R0038-19598 · Mathematically reviewed - [Question 19599: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0099/) · R0038-19599 · Mathematically reviewed - [Question 19600: Validity, Inclusion-Maximality and Global Maximum Are Separate](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261106-r02-clique-and-independent-set-0100/) · R0038-19600 · Mathematically reviewed The source bank retains its original candidate and verification labels. 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