Electronic Theses and Dissertations

Date of Award

1-1-2024

Document Type

Dissertation

Degree Name

Ph.D. in Mathematics

First Advisor

Bing Wei

Second Advisor

Talmage James Reid

Third Advisor

Lei Cao

School

University of Mississippi

Relational Format

dissertation/thesis

Abstract

A graph G is H-saturated if G contains no copy of the graph H, but for any missing edge e of G, there exists a copy of H in G+e. The saturation number of H, denoted by sat(n, H), is the minimal number of edges among all H-saturated graphs with n vertices. The study of saturation number begins with a beautiful result presented by Erdös, Hajnal, and Moon [14] who calculated the saturation number of a complete graph along with the identification of the unique graph achieving this number.

Available for download on Saturday, November 22, 2025

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