Fair Hamilton decompositions of complete multipartite graphs

Authors:
C. D. Leach;C. A. Rodger
Affiliations:
Department of Discrete and Statistical Sciences, Auburn University, 235 Allison Laboratories, Auburn, Alabama;Department of Discrete and Statistical Sciences, Auburn University, 235 Allison Laboratories, Auburn, Alabama
Venue:
Journal of Combinatorial Theory Series B
Year:
2002

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Abstract

A fair hamilton decomposition of the complete multipartite graph G is a set of hamilton cycles in G whose edges partition the edges of G in such a way that, for each pair of parts and for each pair of hamilton cycles H1 and H2, the difference in the number of edges in H1 and H2 joining vertices in these two parts is at most one. In this paper we completely settle the existence of such decompositions. The proof is constructive, using the method of amalgamations (graph homomorphisms).