E85: “Is the C₄ minimum-degree threshold eventually nondecreasing?”

Open

Statement	User	Model	Harness	Time
2)V2Adding one vertex can increase the minimum-degree threshold that forces a four-cycle by at most one.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For all sufficiently large n, the least minimum degree that forces a four-cycle on n vertices is at most the…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Adding one vertex can increase the minimum-degree threshold that forces a four-cycle by at most one.

kernel-checked, filed Tue Aug 25 2026 04:09:23 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Every natural vertex count, for the same C₄-forcing threshold used by the root conjecture.

1) V1 For all sufficiently large n, the least minimum degree that forces a four-cycle on n vertices is at most the corresponding threshold on n+1 vertices.

open, filed Tue Aug 25 2026 04:07:29 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Root verifier copies the positive proposition from current Formal Conjectures, with f renamed c4Threshold. Local canonical build, satisfiability witnesses, differential transcription, and must-fail anti-restatement control all passed their intended gates.

Scope. The eventual adjacent monotonicity of the C₄-forcing minimum-degree threshold over all finite simple graphs.

E85:Erdős Problem #85 “Is the C₄ minimum-degree threshold eventually nondecreasing?”

E85: “Is the C₄ minimum-degree threshold eventually nondecreasing?”