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On the Complexity of the Vertex 3-Coloring Problem for the Hereditary Graph Classes With Forbidden Subgraphs of Small Size

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Abstract

The 3-coloring problem for a given graph consists in verifying whether it is possible to divide the vertex set of the graph into three subsets of pairwise nonadjacent vertices. A complete complexity classification is known for this problem for the hereditary classes defined by triples of forbidden induced subgraphs, each on at most 5 vertices. In this article, the quadruples of forbidden induced subgraphs is under consideration, each on atmost 5 vertices. For all but three corresponding hereditary classes, the computational status of the 3-coloring problem is determined. Considering two of the remaining three classes, we prove their polynomial equivalence and polynomial reducibility to the third class.

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Authors and Affiliations

  1. National Research University Higher School of Economics, ul. Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155, Russia

    D. V. Sirotkin & D. S. Malyshev

  2. Lobachevsky State University of Nizhny Novgorod, pr. Gagarina 23, Nizhny Novgorod, 603950, Russia

    D. V. Sirotkin & D. S. Malyshev

Authors
  1. D. V. Sirotkin
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  2. D. S. Malyshev
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Correspondence to D. V. Sirotkin.

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Original Russian Text © D.V. Sirotkin, D.S. Malyshev, 2018, published in Diskretnyi Analiz i Issledovanie Operatsii, 2018, Vol. 25, No. 4, pp. 112–130.

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Sirotkin, D.V., Malyshev, D.S. On the Complexity of the Vertex 3-Coloring Problem for the Hereditary Graph Classes With Forbidden Subgraphs of Small Size. J. Appl. Ind. Math. 12, 759–769 (2018). https://doi.org/10.1134/S1990478918040166

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  • DOI: https://doi.org/10.1134/S1990478918040166

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