Degree Type

Dissertation

Date of Award

2012

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Ryan Martin

Abstract

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.

Copyright Owner

Jason James Smith

Language

en

Date Available

2012-10-31

File Format

application/pdf

File Size

75 pages

Included in

Mathematics Commons

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