# OCME ยท Knowledge & practice explorer 302 MKO / 1,441 families / 360 batches / 36,000 questions. 36,000 second-context math/bilingual reviewed; 0 display/symbol-checked candidates. Source questions: candidate. English: ai_candidate. No new proof, Lean, SREG or training. 100 results; page 4/4. ## Question 15676: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0051`; number: 15676 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0051/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0051/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0051.json) ## Question 15677: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0052`; number: 15677 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0052/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0052/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0052.json) ## Question 15678: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0053`; number: 15678 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0053/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0053/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0053.json) ## Question 15679: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0054`; number: 15679 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0054/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0054/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0054.json) ## Question 15680: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0055`; number: 15680 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0055/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0055/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0055.json) ## Question 15681: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0056`; number: 15681 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0056/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0056/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0056.json) ## Question 15682: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0057`; number: 15682 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0057/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0057/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0057.json) ## Question 15683: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0058`; number: 15683 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0058/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0058/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0058.json) ## Question 15684: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0059`; number: 15684 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0059/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0059/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0059.json) ## Question 15685: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0060`; number: 15685 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0060/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0060/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0060.json) ## Question 15686: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0061`; number: 15686 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0061/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0061/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0061.json) ## Question 15687: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0062`; number: 15687 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0062/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0062/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0062.json) ## Question 15688: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0063`; number: 15688 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0063/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0063/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0063.json) ## Question 15689: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0064`; number: 15689 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0064/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0064/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0064.json) ## Question 15690: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0065`; number: 15690 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0065/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0065/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0065.json) ## Question 15691: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0066`; number: 15691 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0066/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0066/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0066.json) ## Question 15692: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0067`; number: 15692 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0067/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0067/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0067.json) ## Question 15693: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0068`; number: 15693 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0068/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0068/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0068.json) ## Question 15694: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0069`; number: 15694 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0069/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0069/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0069.json) ## Question 15695: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0070`; number: 15695 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0070/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0070/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0070.json) ## Question 15696: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0071`; number: 15696 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0071/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0071/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0071.json) ## Question 15697: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0072`; number: 15697 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0072/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0072/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0072.json) ## Question 15698: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0073`; number: 15698 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0073/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0073/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0073.json) ## Question 15699: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0074`; number: 15699 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0074/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0074/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0074.json) ## Question 15700: A Nonoptimal Valid Coloring Still Supplies an Upper Bound - ID: `q-20261014-advance-20261031-r05-graph-coloring-0075`; number: 15700 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-upper-bound](/en/explore/?family=qf-mod31-coloring-upper-bound) - Batch: [batch-20261014-advance-20261031-r05-graph-coloring-foundations](/en/explore/?batch=batch-20261014-advance-20261031-r05-graph-coloring-foundations) - [Derivation](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0075/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0075/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0075.json)