Edge Colorings of K(m,n) with m+n-1 Colors Which Forbid Rainbow Cycles
Peter D. Johnson, Claire Zhang · Theory and Applications of Graphs · 2017
For positive integers m, n, the greatest number of colors that can appear in an edge coloring of K(m,n) which avoids rainbow cycles is m + n - 1. Here these colorings are constructively characterized. It turns out that these colorings can be encoded by certain vertex labelings of full binary trees with m + n leafs.