Mathematics Commons^™

On Eulerian Irregularity And Decompositions In Graphs, Eric Andrews

Dissertations

Abstract attached as separate file.

Hamiltonicity, Pancyclicity, And Cycle Extendability In Graphs, Deborah C. Arangno

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A significant portion of Graph Theory is devoted to determining the characteristics which guarantee the existence of long cycles.

Long cycles have roles in applications to civil engineering, chemistry, and communications, among many others, but the problem, in and of itself, of determining whether a graph has a cycle of some fixed and typically large length is one of the most important problems of both pure Mathematics and Computer Science.

A cycle containing all the vertices of the graph is called a Hamiltonian cycle, and a graph which possesses such a cycle is said to be Hamiltonian. If …

Strong Chromatic Index Of Subset Graphs, Jennifer Quinn, Arthur Benjamin

Jennifer J. Quinn

The strong chromatic index of a graph G, denoted sq(G), is the minimum number of parts needed to partition the edges of G into induced matchings. For 0 ≤ k ≤ l ≤ m, the subset graph Sm(k, l) is a bipartite graph whose vertices are the k- and l-subsets of an m element ground set where two vertices are adjacent if and only if one subset is contained in the other. We show that sq(Sm(k, l) ) = m choose l-k and that this number satisfies the strong chromatic index conjecture by Brualdi and Quinn for bipartite graphs. Further, …