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
Applied and Computational Mathematics (MS)
Department, Program, or Center
School of Mathematical Sciences (COS)
Sullivan, Eric C., "Minimum saturated subgraphs of tripartite graphs" (2014). Thesis. Rochester Institute of Technology. Accessed from
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