Date of Award
Doctor of Philosophy
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.
Jason James Smith
Smith, Jason James, "Induced Saturation Number" (2012). Graduate Theses and Dissertations. 12465.