# OCME · 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.

25 results; page 1/1.

## Question 15626: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0001`; number: 15626
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0001/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0001/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0001.json)

## Question 15627: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0002`; number: 15627
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0002/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0002/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0002.json)

## Question 15628: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0003`; number: 15628
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0003/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0003/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0003.json)

## Question 15629: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0004`; number: 15629
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0004/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0004/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0004.json)

## Question 15630: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0005`; number: 15630
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0005/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0005/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0005.json)

## Question 15631: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0006`; number: 15631
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0006/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0006/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0006.json)

## Question 15632: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0007`; number: 15632
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0007/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0007/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0007.json)

## Question 15633: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0008`; number: 15633
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0008/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0008/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0008.json)

## Question 15634: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0009`; number: 15634
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0009/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0009/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0009.json)

## Question 15635: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0010`; number: 15635
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0010/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0010/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0010.json)

## Question 15636: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0011`; number: 15636
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0011/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0011/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0011.json)

## Question 15637: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0012`; number: 15637
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0012/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0012/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0012.json)

## Question 15638: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0013`; number: 15638
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0013/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0013/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0013.json)

## Question 15639: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0014`; number: 15639
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0014/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0014/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0014.json)

## Question 15640: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0015`; number: 15640
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0015/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0015/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0015.json)

## Question 15641: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0016`; number: 15641
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0016/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0016/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0016.json)

## Question 15642: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0017`; number: 15642
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0017/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0017/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0017.json)

## Question 15643: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0018`; number: 15643
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0018/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0018/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0018.json)

## Question 15644: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0019`; number: 15644
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0019/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0019/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0019.json)

## Question 15645: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0020`; number: 15645
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0020/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0020/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0020.json)

## Question 15646: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0021`; number: 15646
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0021/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0021/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0021.json)

## Question 15647: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0022`; number: 15647
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0022/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0022/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0022.json)

## Question 15648: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0023`; number: 15648
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0023/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0023/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0023.json)

## Question 15649: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0024`; number: 15649
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0024/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0024/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0024.json)

## Question 15650: Proper k-Coloring Means Edge Properness and At Most k Used Labels

- ID: `q-20261014-advance-20261031-r05-graph-coloring-0025`; number: 15650
- Processing: second_context_reviewed
- MKO: [mko-graph-coloring](/en/mko/mko-graph-coloring/)
- Family: [qf-mod31-coloring-proper-audit](/en/explore/?family=qf-mod31-coloring-proper-audit)
- 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-0025/) / [Markdown](/en/questions/q-20261014-advance-20261031-r05-graph-coloring-0025/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261031-r05-graph-coloring-0025.json)