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Complete Complexity Dichotomy for \(\boldsymbol 7 \)-Edge Forbidden Subgraphs in the Edge Coloring Problem

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Abstract

The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most \(6\) edges. We improve this result and obtain a complete complexity classification of the edge coloring problem for all sets of prohibitions each of which has at most \(7\) edges.

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Funding

The author was supported by the Russian Science Foundation (project no. 19–71–00005).

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Authors and Affiliations

  1. National Research University “Higher School of Economics”, Nizhny Novgorod, 603155, Russia

    D. S. Malyshev

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  1. D. S. Malyshev
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Correspondence to D. S. Malyshev.

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Translated by Ya.A. Kopylov

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Malyshev, D.S. Complete Complexity Dichotomy for \(\boldsymbol 7 \)-Edge Forbidden Subgraphs in the Edge Coloring Problem. J. Appl. Ind. Math. 14, 706–721 (2020). https://doi.org/10.1134/S1990478920040092

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