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Edge Colorings Of Complete Multipartite Graphs Forbidding Rainbow Cycles, Peter Johnson, Andrew Owens
Edge Colorings Of Complete Multipartite Graphs Forbidding Rainbow Cycles, Peter Johnson, Andrew Owens
Theory and Applications of Graphs
It is well known that if the edges of a finite simple connected graph on n vertices are colored so that no cycle is rainbow, then no more than n-1 colors can appear on the edges. In previous work it has been shown that the essentially different rainbow-cycle-forbidding edge colorings of Kn with n-1 colors appearing are in 1-1 correspondence with (can be encoded by) the (isomorphism classes of) full binary trees with n leafs. In the encoding, the natural Huffman labeling of each tree arising from the assignment of 1 to each leaf plays a role. Very recently …