Date of Award
Master of Science (MS)
College of Science and Mathematics
Thesis Sponsor/Dissertation Chair/Project Chair
Graph coloring, Homomorphisms (Mathematics)
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.
Jakubowski, Matthew, "Partial Colorings of Graphs" (2014). Theses, Dissertations and Culminating Projects. 432.