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Triangle-free graphs with large chromatic numbers

By A. Nilli

Abstract

AbstractIt is shown that there are two positive constants c1,c2 such that the maximum possible chromatic number of a triangle-free graph with m>1 edges is at most c1m1/3/(logm)2/3 and at least c2m1/3/(logm)2/3. This is deduced from results of Ajtai, Komlós, Szemerédi, Kim and Johansson, and settles a problem of Erdős

Publisher: Elsevier Science B.V.
Year: 2000
DOI identifier: 10.1016/S0012-365X(99)00109-0
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