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
mathramsey-theory
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