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Cographs and 1-Sums

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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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Acknowledgements

The author thanks James Oxley for helpful suggestions. The author also thanks Thomas Zaslavsky for helpful discussions.

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The author declares that no funds or grants were received during the preparation of this manuscript.

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  1. Department of Mathematics and Statistics, Binghamton University, Binghamton, NY, USA

    Jagdeep Singh

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  1. Jagdeep Singh
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Correspondence to Jagdeep Singh.

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Singh, J. Cographs and 1-Sums. Graphs and Combinatorics 40, 2 (2024). https://doi.org/10.1007/s00373-023-02730-z

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  • DOI: https://doi.org/10.1007/s00373-023-02730-z

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