Discrete Mathematics & Theoretical Computer Science, Vol 5 (2002)

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Multicolored isomorphic spanning trees in complete graphs

Gregory Constantine


Can a complete graph on an even number n (>4) of vertices be properly edge-colored with n-1 colors in such a way that the edges can be partitioned into edge disjoint colorful isomorphic spanning trees? A spanning treee is colorful if all n-1 colors occur among its edges. It is proved that this is possible to accomplish whenever n is a power of two, or five times a power of two.

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