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Diskretnyi Analiz i Issledovanie Operatsii, 2023, Volume 30, Issue 4, Pages 91–109
DOI: https://doi.org/10.33048/daio.2023.30.758 (Mi da1335) 		 
A complete complexity dichotomy of the edge-coloring problem for all sets of 8-edge forbidden subgraphs

D. S. Malyshevab, O. I. Duginovc

a National Research University “Higher School of Economics”, 25/12 Bolshaya Pechyorskaya Street, 603155 Nizhny Novgorod, Russia
b Lobachevsky Nizhny Novgorod State University, 23 Gagarin Avenue, 603950 Nizhny Novgorod, Russia
c Belarusian State University, 4 Nezavisimost Avenue, 220030 Minsk, Belarus
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DOI: https://doi.org/10.33048/daio.2023.30.758
Abstract: For a given graph, the edge-coloring problem is to minimize the number of colors sufficient to color all the graph edges so that any adjacent edges receive different colors. For all classes defined by sets of forbidden subgraphs, each with 7 edges, the complexity status of this problem is known. In this paper, we obtain a similar result for all sets of 8-edge prohibitions. Illustr. 2, bibliogr. 38.
Keywords: edge-coloring problem, computational complexity, monotone class.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-04001
Russian Science Foundation 21-11-00194
Belarusian Republican Foundation for Fundamental Research Ф21РМ-001
Sections 2 and 3 have been obtained with the support of the Russian Foundation for Basic Research and the Belarusian Republic Foundation for Basic Research, project no. 20-51-04001 (F21RM-001). Sections 4 and 5 were supported by the Russian Science Foundation, project no. 21-11-00194, https://rscf.ru/en/project/21-11-00194/.
Received: 24.11.2022
Revised: 10.06.2023
Accepted: 22.06.2023
English version:
Journal of Applied and Industrial Mathematics, 2023, Volume 17, Issue 4, Pages 791–801
DOI: https://doi.org/10.1134/S1990478923040099
Document Type: Article
UDC: 519.17
Language: Russian
Citation: D. S. Malyshev, O. I. Duginov, “A complete complexity dichotomy of the edge-coloring problem for all sets of 8-edge forbidden subgraphs”, Diskretn. Anal. Issled. Oper., 30:4 (2023), 91–109; J. Appl. Industr. Math., 17:4 (2023), 791–801
Citation in format AMSBIB
\Bibitem{MalDug23}
\by D.~S.~Malyshev, O.~I.~Duginov
\paper A complete complexity dichotomy of~the~edge-coloring problem for~all~sets~of~8-edge forbidden subgraphs
\jour Diskretn. Anal. Issled. Oper.
\yr 2023
\vol 30
\issue 4
\pages 91--109
\mathnet{http://mi.mathnet.ru/da1335}
\transl
\jour J. Appl. Industr. Math.
\yr 2023
\vol 17
\issue 4
\pages 791--801
\crossref{https://doi.org/10.1134/S1990478923040099}
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