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arXiv · 2210.04139

Cographs and 1-sums

Jagdeep Singh
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Abstract

A graph that can be generated from $K_1$ using joins and 0-sums is called a cograph. We define a sesquicograph to be a graph that can be generated from $K_1$ using joins, 0-sums, and 1-sums. We show that, like cographs, sesquicographs are closed under induced minors. Cographs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. We obtain an analogue of this result for sesquicographs, that is, we find those non-sesquicographs for which every proper induced subgraph is a sesquicograph.

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Jagdeep Singh. 2022-10-09. Cographs and 1-sums. https://arxiv.org/abs/2210.04139

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