Abstract

Let F and H be graphs. A subgraph G of H is an F-saturated subgraph of H if F is not a subgraph of G and F is a subgraph of G+e for any edge e in E(H) E(G). The saturation number of F in H is the minimum number of edges in a F-saturated subgraph of H. We denote the saturation number of F in H as sat(H,F). In this thesis we review the history of saturated subgraphs, and prove new results on saturated subgraphs of tripartite graphs. Let Ka,b,c be a compete tripartite graph, with partite sets of size a, b, and c. Specifically, we determine sat(Kn1,n2,n3,Kl,l,l), for n1≥ n2≥ n3, when n2 bounded by a linear function of n3. We also examine the special case when l=1 and determine sat(Kn1,n2,n3,K3)$ for n1≥ n2≥ n3, and n_3 sufficiently large. We also consider two natural variants of saturated subgraphs that arise in the tripartite setting. We examine the behavior of these extensions using illustrative examples to highlight the differences between these variations and the original problem.

Library of Congress Subject Headings

Graph theory

Publication Date

5-12-2014

Document Type

Thesis

Student Type

Graduate

Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)

Advisor

Paul Wenger

Advisor/Committee Member

Jobby Jacob

Advisor/Committee Member

Darren Narayan

Comments

Physical copy available from RIT's Wallace Library at QA166 .S85 2014

Campus

RIT – Main Campus

Plan Codes

ACMTH-MS

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