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.
|Commitee:||Axenovich, Maria, Hogben, Leslie, Long, Ling, Lutz, Jack|
|School:||Iowa State University|
|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|
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