Almost partitioning a 3-edge-coloured $K_{n,n}$ into 5 monochromatic cycles

Richard Lang, Oliver Schaudt, Maya Stein

Published 2015-09-30Version 1

We show that for any colouring of the edges of the complete bipartite graph $K_{n,n}$ with 3 colours there are 5 disjoint monochromatic cycles which together cover all but $o(n)$ of the vertices and 18 disjoint monochromatic cycles which together cover all vertices.