Partitioning Complete Bipartite Graphs by Monochromatic Cycles

For every positive integerrthere exists a constantCrdepending only onrsuch that for every colouring of the edges of the complete bipartite graphKn, nwithrcolours, there exists a set of at mostCrmonochromatic cycles whose vertex sets partition the vertex set ofKn, n. This answers a question raised by Erdős, Gyárfás, and Pyber.