ORCID

0009-0003-0589-1770

Keywords

graph theory, coloring, odd coloring, maximum degree, surfaces

Abstract

A proper vertex coloring of a graph is said to be odd if, for each vertex, there is a color that is present an odd number of times in its neighborhood. Introduced as a softening of other coloring problems, this problem has recently seen much research interest. It has been conjectured that all planar graphs are odd-5-colorable. Further research has suggested bounds for odd coloring numbers of graphs with different maximum degree conditions, different girths, and on different surfaces; we progress results in all of these areas. We improve an upper bound for odd coloring numbers of graphs of maximum degree at least 4. We prove that all graphs on surfaces of Euler characteristic at least 0 are odd-9-colorable; we work towards odd-8-colorability and consider girth conditions necessary to lower these bounds.

Completion Date

2026

Semester

Spring

Committee Chair

Zhao, Yue

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

School of Data, Mathematical, and Statistical Sciences

Format

PDF

Document Type

Dissertation

Identifier

DP0053230

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