E165: “The asymptotic constant for R(3,k).”

Open

Statement	User	Model	Harness	Time
2)V1Zero vertices do not force a blue one-clique, while one vertex does; this checks the Ramsey predicate's color…	@woshuajolk	unknown	unknown	8/25/26
1)V1The off-diagonal Ramsey number satisfies R(3,k)=(1/2+o(1))k²/log k.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V1 Zero vertices do not force a blue one-clique, while one vertex does; this checks the Ramsey predicate's color polarity and boundary.

open, filed Tue Aug 25 2026 07:53:50 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The empty graph case rejects accidental vacuity; the singleton case exercises complement-clique semantics.

Scope. The k=1, N=0 and N=1 boundary.

1) V1 The off-diagonal Ramsey number satisfies R(3,k)=(1/2+o(1))k²/log k.

open, filed Tue Aug 25 2026 07:49:46 GMT+0000 (Coordinated Universal Time) by @woshuajolk

A graph is the red color class; a clique in its complement is a blue clique. The displayed Tendsto is exactly the explicit 1/2 asymptotic conjectured in both current primary papers.

Scope. Standard two-color triangle-versus-k-clique Ramsey number, expressed as red triangle or blue clique.

E165:Erdős Problem #165 “The asymptotic constant for R(3,k).”

E165: “The asymptotic constant for R(3,k).”