Mathematics Commons^™

Edge Colorings Of Graphs And Their Applications, Daniel Johnston

Dissertations

Edge colorings have appeared in a variety of contexts in graph theory. In this work, we study problems occurring in three separate settings of edge colorings.

For more than a quarter century, edge colorings have been studied that induce vertex colorings in some manner. One research topic we investigate concerns edge colorings belonging to this class of problems. By a twin edge coloring of a graph G is meant a proper edge coloring of G whose colors come from the integers modulo k that induce a proper vertex coloring in which the color of a vertex is the sum of …

Phantom Maps, Decomposability, And Spaces Meeting Particular Finiteness Conditions, James Schwass

Dissertations

The purpose of this dissertation is to extend principles for detecting the existence of essential phantom maps into spaces meeting particular finiteness conditions. Zabrodsky shows that a space Y having the homotopy type of a finite CW complex is the target of essential phantom maps if and only if Y has a nontrivial rational homology group. We show this observation holds on the collection of finite generalized CW complexes. Similarly, Iriye shows a finite-type, simply connected suspension space is the target of essential phantom maps if and only if it has a nontrivial rational homology group. We show this observation …