Monochromatic cycle partitions of edge-colored graphs

Abstract

In this article we study the monochromatic cycle partition problem for non-complete graphs. We consider graphs with a given independence number α(G) = α. Generalizing a classical conjecture of Erdös, Gyárfás and Pyber, we conjecture that if we r-color the edges of a graph G with α(G) = α, then the vertex set of G can be partitioned into at most αr vertex disjoint monochromatic cycles. In the direction of this conjecture we show that under these conditions the vertex set of G can be partitioned into at most 25(αr)2log(αr) vertex disjoint monochromatic cycles. © 2010 Wiley Periodicals, Inc. J Graph Theory 66: 57–64, 2010