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The Complexity of the Vertex 3-Colorability Problem for Some Hereditary Classes Defined By 5-Vertex Forbidden Induced Subgraphs

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Abstract

We completely determine the complexity status of the vertex 3-colorability problem for the problem restricted to all hereditary classes defined by at most 3 forbidden induced subgraphs each on at most 5 vertices. We also present a complexity dichotomy for the problem and the family of all hereditary classes defined by forbidding an induced bull and any set of induced subgraphs each on at most 5 vertices.

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Acknowledgements

The research is partially supported by Russian Foundation for Basic Research, grant No 16-31-60008-mol-a-dk; by RF President grant MK-4819.2016.1; by LATNA laboratory, National Research University Higher School of Economics. The author would like to thank anonymous reviewers for their valuable comments.

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  1. National Research University Higher School of Economics, 25/12 Bolshaja Pecherskaja Ulitsa, Nizhny Novgorod, 603155, Russia

    D. S. Malyshev

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Malyshev, D.S. The Complexity of the Vertex 3-Colorability Problem for Some Hereditary Classes Defined By 5-Vertex Forbidden Induced Subgraphs. Graphs and Combinatorics 33, 1009–1022 (2017). https://doi.org/10.1007/s00373-017-1790-7

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  • DOI: https://doi.org/10.1007/s00373-017-1790-7

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