Dissertation/Thesis Abstract

Induced saturation number
by Smith, Jason James, Ph.D., Iowa State University, 2012, 75; 3511472
Abstract (Summary)

In this paper, we discuss the induced saturation number. It is a nice generalization of the saturation number that will allow us to consider induced subgraphs. We define the induced saturation number of a graph H to be the fewest number of gray edges in a trigraph T such that H does not appear in any realization of T, but if a black or white edge of T is flipped to gray then there exists a realization of T with H as an induced subgraph. We will provide some general results as well as the result for a path on four vertices. We will also discuss the injective coloring number and a generalization of that.

Indexing (document details)
Advisor: Martin, Ryan
Commitee: Axenovich, Maria, Hogben, Leslie, Long, Ling, Lutz, Jack
School: Iowa State University
Department: Mathematics
School Location: United States -- Iowa
Source: DAI-B 73/10(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Mathematics
Keywords: Graph theory, Indsat, Induced subgraphs, Injective coloring, Saturation number
Publication Number: 3511472
ISBN: 9781267392817
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