Maximal Sets of Hamilton Cycles in Complete Multipartite Graphs

Abstract

A set of S edge-disjoint hamilton cycles in a graph G is said to be maximal if the hamilton cycles in S form a subgraph of G such that G-E(S) has no hamilton cycle. The set of integers m for which a graph G contains a maximal set of m edge-disjoint hamilton cycles has previously been determined whenever G is a complete graph, a complete bipartite graph, and in many cases when G is a complete multipartite graph. In this dissertation, some of the remaining open cases regarding complete multipartite graphs will be resolved.