Multicolored isomorphic spanning trees in complete graphs

Gregory Constantine (1)

1 Department of Mathematics [Pittsburgh]

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.

Mots clés: Orthogonal Latin squares; colorful matching; multicolored tree

Domaines: Mathématique discrète [cs.DM]

Gregory Constantine. Multicolored isomorphic spanning trees in complete graphs. Discrete Mathematics and Theoretical Computer Science, 2002, Vol. 5, pp.121-126. ⟨10.46298/dmtcs.306⟩. ⟨hal-00958977⟩