An improved bound for the monochromatic cycle partition number

Improving a result of Erdős, Gyárfás and Pyber for large n we show that for every integer r ⩾ 2 there exists a constant n 0 = n 0 ( r ) such that if n ⩾ n 0 and the edges of the complete graph K n are colored with r colors then the vertex set of K n can be partitioned into at most 100 r log r vertex disjoint monochromatic cycles.