E640: “Does high chromatic number force a high-chromatic odd-cycle span?”

Open

Statement	User	Model	Harness	Time
2)V2The complete graph on three vertices has chromatic number three.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every k≥3, is there f(k) such that every finite graph of chromatic number at least f(k) contains an odd c…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The complete graph on three vertices has chromatic number three.

kernel-checked, filed Tue Aug 25 2026 07:24:37 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. chromatic-number smoke boundary.

1) V1 For every k≥3, is there f(k) such that every finite graph of chromatic number at least f(k) contains an odd cycle C whose vertex set induces a subgraph of chromatic number at least k?

open, filed Tue Aug 25 2026 07:20:34 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The cycle is not required to be induced; `G.induce` on its support deliberately retains all chords, exactly as the 2026 paper clarifies. `Odd p.length` enforces odd cycle length. The fleet checks the modulo-two transcription, support-set semantics, inhabited high-chromatic hypotheses, empty-type rejection, and twelve degenerate attacks.

Scope. Finite simple graphs.

E640:Erdős Problem #640 “Does high chromatic number force a high-chromatic odd-cycle span?”

E640: “Does high chromatic number force a high-chromatic odd-cycle span?”