Semester
Summer
Date of Graduation
2021
Document Type
Thesis
Degree Type
PhD
College
Eberly College of Arts and Sciences
Department
Mathematics
Committee Chair
Hong-Jian Lai
Committee Member
John Goldwasser
Committee Member
Guodong Guo
Committee Member
Rong Luo
Committee Member
Jerzy Wojciechowski
Abstract
This dissertation proves a collection of results in some heterogeneous generalizations of vertex coloring, i.e. generalizations in which the relationship between the colors of two adjacent vertices may differ throughout the graph. For the most part, the results are from group coloring, group list coloring, and DP coloring. The main results are as follows: a group list coloring analogue of Brooks' Theorem for multigraphs, a result linking group structure (rather than only group size) with group coloring, some results involving coloring edge-disjoint unions, and an examination of the relationship between the group and DP coloring numbers of a multigraph and its simplification.
Recommended Citation
Mazza, Lucian Ciletti, "Heterogeneous Generalizations of Vertex Coloring" (2021). Graduate Theses, Dissertations, and Problem Reports. 8325.
https://researchrepository.wvu.edu/etd/8325