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Hamilton Decompositions Of 6-Regular Abelian Cayley Graphs, Erik E. Westlund

Dissertations, Master's Theses and Master's Reports - Open

In 1969, Lovasz asked whether every connected, vertex-transitive graph has a Hamilton path. This question has generated a considerable amount of interest, yet remains vastly open. To date, there exist no known connected, vertex-transitive graph that does not possess a Hamilton path. For the Cayley graphs, a subclass of vertex-transitive graphs, the following conjecture was made:

Weak Lovász Conjecture: Every nontrivial, finite, connected Cayley graph is hamiltonian.

The Chen-Quimpo Theorem proves that Cayley graphs on abelian groups flourish with Hamilton cycles, thus prompting Alspach to make the following conjecture:

Alspach Conjecture: Every 2k-regular, connected Cayley graph on a …

Edge Coloring Bibds And Constructing Moelrs , John S. Asplund

Dissertations, Master's Theses and Master's Reports - Open

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Some historical uses and background are touched upon as well. The majority of the definitions are contained within this chapter as well.

In Chapter 2 we consider the question whether one can decompose λ copies of monochromatic K_v into copies of K_k such that each copy of the K_k contains at most one edge from each K_v. This is called a proper edge coloring (Hurd, Sarvate, [29]). The majority of the content in this section is a wide variety of …