Around a conjecture of ErdH{o}s on graph Ramsey numbers
Combinatorics
2012-11-28 v1
Abstract
For given graphs G1 and G2 the Ramsey number R(G1,G2), is the smallest positive integer n such that each blue-red edge coloring of the complete graph Kn contains a blue copy of G1 or a red copy of G2. In 1983, Erdos conjectured that there is an absolute constant c such that R(G) = R(G,G) < 2c p m for any graph G with m edges and no isolated vertices. Recently this conjecture was proved by B. Sudakov. In this note, using the Sudakovs ideas we give an extension of his result and some interesting corollaries.
Cite
@article{arxiv.1211.6287,
title = {Around a conjecture of ErdH{o}s on graph Ramsey numbers},
author = {Leila Maherani and Gholamreza Omidi},
journal= {arXiv preprint arXiv:1211.6287},
year = {2012}
}
Comments
arXiv admin note: text overlap with arXiv:1002.0095 by other authors