An improved bound for the monochromatic cycle partition number

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Abstract

Improving a result of Erdős, Gyárfás and Pyber for large n we show that for every integer r2 there exists a constant n0=n0(r) such that if nn0 and the edges of the complete graph Kn are colored with r colors then the vertex set of Kn can be partitioned into at most 100rlogr vertex disjoint monochromatic cycles.

Keywords

Edge colorings
Monochromatic partitions
Regularity Lemma

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1

Research supported in part by OTKA Grants T038198 and T046234.

2

Research supported in part by the National Science Foundation under Grant No. DMS-0456401.