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An improved upper bound for Ramsey number N (3, 3, 3, 3; 2)

✍ Scribed by Adolfo Sanchez-Flores

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 251 KB
Volume: 140
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0187-9

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✦ Synopsis

The Ramsey number N(3, 3, 3, 3; 2) is the smallest integer n such that each 4-coloring by edges of the complete graph on n vertices contains monochromatic triangles. It is well known that 51 ~< N(3,3,3,3;2) ~< 65. Here we prove that N(3,3,3,3;2) ~< 64.

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## Abstract For every __r__‐graph __G__ let π(__G__) be the minimal real number ϵ such that for every ϵ < 0 and __n__ ϵ __n__~0~(λ, __G__) every __R__‐graph __H__ with __n__ vertices and more than (π + ϵ)(nr) edges contains a copy of __G__. The real number λ(__G__) is defined in the same way, addin