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
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
Recommended Citation
Jakubowski, Matthew, "Partial Colorings of Graphs" (2014). Theses, Dissertations and Culminating Projects. 432.
https://digitalcommons.montclair.edu/etd/432