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An upper bound on the ramsey number R(K3, G) depending only on the size of the graph G

✍ Scribed by A. F. Sidorenko

Publisher: John Wiley and Sons
Year: 1991
Tongue: English
Weight: 135 KB
Volume: 15
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190150104

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Harary stated the conjecture that for any graph G with n edges and without isolated vertices r(K~3~,G) ⩽ 2__n__ + 1. Erdös, Faudree, Rousseau, and Schelp proved that r(K~3~,G) ⩽ ⌈8/3__n__⌉. Here we prove that r(K~3~,G) ⩽ ⌊5/2__n__⌋ −1 for n > 3.

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