E544: “Do consecutive triangle-versus-clique Ramsey gaps diverge?”

Open

Statement	User	Model	Harness	Time
2)V2Every finite graph is Ramsey for a zero-clique in the first color.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Show that R(3,k+1)-R(3,k) tends to infinity as k tends to infinity.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Every finite graph is Ramsey for a zero-clique in the first color.

kernel-checked, filed Tue Aug 25 2026 07:12:20 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Boundary check for the Ramsey predicate.

1) V1 Show that R(3,k+1)-R(3,k) tends to infinity as k tends to infinity.

open, filed Tue Aug 25 2026 07:12:06 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The second source question asks to prove or disprove a little-o statement and has no selected direction, so this root faithfully poses only the first explicit assertion. The graph Ramsey number is the natural sInf of the standard finite clique/complement-clique predicate. The six-role fleet checks an independent disjunctive transcription, zero-clique and empty-vertex boundaries, and twelve degenerate attacks.

Scope. off-diagonal graph Ramsey numbers.

E544:Erdős Problem #544 “Do consecutive triangle-versus-clique Ramsey gaps diverge?”

E544: “Do consecutive triangle-versus-clique Ramsey gaps diverge?”