Title

Ramsey numbers for sparse graphs

Document Type

Article

Date of Original Version

1-1-1998

Abstract

We consider a class of graphs on n vertices, called (d, f)-arrangeable graphs. This class of graphs contains all graphs of bounded degree d, and all df-arrangeable graphs, a class introduced by Chen and Schelp in 1993. In 1992, a variation of the Regularity Lemma of Szemerédi was introduced by Eaton and Rödl. As an application of this lemma, we give a linear upper bound, c(d, f)n, for the Ramsey number of graphs in this class, where log2 log2 c(d, f) = 24df5. This improves the earlier result, given in 1983 by Chvátal et al. of a linear bound on the Ramsey number of graphs with bounded degree d, where the constant term was more that a tower of d 2's, and later extended by Chen and Schelp to include d-arrangeable graphs. © 1998 Elsevier Science B.V. All rights reserved.

Publication Title

Discrete Mathematics

Volume

185

Issue

1-3

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