Induced Saturation Number

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2012-01-01
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Smith, Jason
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Ryan Martin
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Altmetrics
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Mathematics
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.

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Sun Jan 01 00:00:00 UTC 2012