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.

Source : oai:HAL:hal-00958977v1

Volume: Vol. 5

Published on: January 1, 2002

Submitted on: March 26, 2015

Keywords: multicolored tree,Orthogonal Latin squares,colorful matching,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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