Hamilton Cycles In Multipartite Graphs With Two Associative Classes

Abstract

In this dissertation, the following two problems are considered: the embedding problem of when a k-edge-coloring of a multipartite graph G can be embedded into a Hamilton decomposition of multipartite graph H containing G; and the existence problem of when there exists a maximal set of t edge-disjoint Hamilton cycles in multipartite graph G. Both results proved make use of the method of amalgamations.