Date of Award

5-2014

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Jonathan Cutler

Committee Member

Aihua Li

Committee Member

Diana Thomas

Subject(s)

Graph coloring, Homomorphisms (Mathematics)

Abstract

Recently, there has been great interest in counting the number of homomorphisms from a graph G into a fixed image graph H. For this thesis, we let H be a complete graph on three vertices with exactly one looped vertex. Homomorphisms from a graph G to this H correspond to partial proper two-colorings of the vertices of G. We are mainly interested in finding which graphs maximize the number of partial two-colorings given a graph with n vertices and m edges. The general result is given for all graphs with m < n -1 as well as basic enumerative results for some very common graphs.

File Format

PDF

Included in

Mathematics Commons

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