# 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 3/4. ## Question 15651: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0076`; number: 15651 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0076/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0076/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0076.json) ## Question 15652: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0077`; number: 15652 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0077/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0077/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0077.json) ## Question 15653: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0078`; number: 15653 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0078/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0078/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0078.json) ## Question 15654: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0079`; number: 15654 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0079/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0079/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0079.json) ## Question 15655: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0080`; number: 15655 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0080/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0080/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0080.json) ## Question 15656: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0081`; number: 15656 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0081/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0081/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0081.json) ## Question 15657: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0082`; number: 15657 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0082/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0082/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0082.json) ## Question 15658: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0083`; number: 15658 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0083/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0083/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0083.json) ## Question 15659: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0084`; number: 15659 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0084/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0084/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0084.json) ## Question 15660: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0085`; number: 15660 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0085/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0085/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0085.json) ## Question 15661: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0086`; number: 15661 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0086/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0086/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0086.json) ## Question 15662: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0087`; number: 15662 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0087/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0087/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0087.json) ## Question 15663: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0088`; number: 15663 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0088/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0088/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0088.json) ## Question 15664: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0089`; number: 15664 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0089/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0089/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0089.json) ## Question 15665: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0090`; number: 15665 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0090/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0090/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0090.json) ## Question 15666: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0091`; number: 15666 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0091/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0091/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0091.json) ## Question 15667: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0092`; number: 15667 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0092/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0092/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0092.json) ## Question 15668: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0093`; number: 15668 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0093/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0093/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0093.json) ## Question 15669: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0094`; number: 15669 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0094/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0094/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0094.json) ## Question 15670: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0095`; number: 15670 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0095/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0095/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0095.json) ## Question 15671: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0096`; number: 15671 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0096/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0096/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0096.json) ## Question 15672: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0097`; number: 15672 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0097/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0097/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0097.json) ## Question 15673: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0098`; number: 15673 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0098/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0098/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0098.json) ## Question 15674: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0099`; number: 15674 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0099/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0099/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0099.json) ## Question 15675: Injective Renaming of Used Colors Preserves the Vertex Partition - ID: `q-20261014-advance-20261031-r05-graph-coloring-0100`; number: 15675 - Processing: second_context_reviewed - MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/) - Family: [qf-mod31-coloring-relabel-invariance](/en/explore/?family=qf-mod31-coloring-relabel-invariance) - 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-0100/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0100/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0100.json) [Next](/en/explore/index.md?mko=mko-graph-coloring&page=4)