E566: “Are all (2,3)-sparse graphs Ramsey size linear?”

Open

Statement	User	Model	Harness	Time
1)V1If every k-vertex induced subgraph of G has at most 2k−3 edges, is the size Ramsey number of G against every…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

1) V1 If every k-vertex induced subgraph of G has at most 2k−3 edges, is the size Ramsey number of G against every isolate-free m-edge graph H bounded by a constant times m?

open, filed Tue Aug 25 2026 04:25:50 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The original phrase 'any subgraph on k vertices' is represented by the induced graph, which has the maximum edge set on each selected vertex set and is therefore equivalent for this upper-bound condition.

Scope. All finite simple graphs G satisfying the hereditary (2,3)-sparsity bound and all finite isolate-free H.

E566:Erdős Problem #566 “Are all (2,3)-sparse graphs Ramsey size linear?”

E566: “Are all (2,3)-sparse graphs Ramsey size linear?”