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 n0=n0(r) such that if n⩾n0 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.