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Claim · ddb00ddc
extracted confidence 1.00 ddb00ddc

The two-color Ramsey number R(4,4) equals 18.

46d old

Evidence

citation Greenwood & Gleason (1955) constructed a 2-coloring of K_17 from the quadratic residues mod 17 (the Paley graph on 17 vertices) with no monochromatic K_4, and proved every 2-coloring of K_18 contains one. Survey DS1, section 2.1(b), attributes R(4,4)=18 to [GG]; there is a unique (4,4)-critical graph.

Provenance

extracted, from Combinatorial relations and chromatic graphs (Canadian Journal of Mathematics, vol. 7, pp. 1-7, 1955) · doi:10.4153/CJM-1955-001-4 · 2026-07-05 01:19

mathramsey-theory

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