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Diskretnyi Analiz i Issledovanie Operatsii, 2020, Volume 27, Issue 3, Pages 71–87
DOI: https://doi.org/10.33048/daio.2020.27.668 (Mi da957) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Efficient solvability of the weighted vertex coloring problem for some hereditary class of graphs with $5$-vertex prohibitions

D. V. Gribanovab, D. S. Malyshevab, D. B. Mokeevba

a National Research University “Higher School of Economics”, 25/12 Bolshaya Pechyorskaya Street, 603155 Nizhny Novgorod, Russia
b Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Avenue, 603950 Nizhny Novgorod, Russia
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DOI: https://doi.org/10.33048/daio.2020.27.668
Abstract: We consider the problem of minimizing the number of colors in the colorings of the vertices of a given graph so that, to each vertex there is assigned some set of colors whose number is equal to the given weight of the vertex; and adjacent vertices receive disjoint sets. For all hereditary classes defined by a pair of forbidden induced connected subgraphs on $5$ vertices but four cases, the computational complexity of the weighted vertex coloring problem with unit weights is known. We prove the polynomial solvability on the sum of the vertex weights for this problem and the intersection of two of the four open cases. We hope that our result will be helpful in resolving the computational complexity of the weighted vertex coloring problem in the above-mentioned forbidden subgraphs. Illustr. 1, bibliogr. 18.
Keywords: weighted vertex coloring problem, hereditary class, computational complexity.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-20001-мол-а-вед
This research is supported by the Russian Foundation for Basic Research (Project 18–31–20001-mol-a-ved).
Received: 25.07.2019
Revised: 06.01.2020
Accepted: 19.02.2020
English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 3, Pages 480–489
DOI: https://doi.org/10.1134/S1990478920030072
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: Russian
Citation: D. V. Gribanov, D. S. Malyshev, D. B. Mokeev, “Efficient solvability of the weighted vertex coloring problem for some hereditary class of graphs with $5$-vertex prohibitions”, Diskretn. Anal. Issled. Oper., 27:3 (2020), 71–87; J. Appl. Industr. Math., 14:3 (2020), 480–489
Citation in format AMSBIB
\Bibitem{GriMalMok20}
\by D.~V.~Gribanov, D.~S.~Malyshev, D.~B.~Mokeev
\paper Efficient solvability of the weighted vertex coloring problem for some hereditary class of~graphs with $5$-vertex prohibitions
\jour Diskretn. Anal. Issled. Oper.
\yr 2020
\vol 27
\issue 3
\pages 71--87
\mathnet{http://mi.mathnet.ru/da957}
\crossref{https://doi.org/10.33048/daio.2020.27.668}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 3
\pages 480--489
\crossref{https://doi.org/10.1134/S1990478920030072}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85094681258}
Linking options:
  • https://www.mathnet.ru/eng/da957
  • https://www.mathnet.ru/eng/da/v27/i3/p71
    • This publication is cited in the following articles:
    1. O. O. Razvenskaya, D. S. Malyshev, “Efficient solvability of the weighted vertex coloring problem for some two hereditary graph classes”, J. Appl. Industr. Math., 15:1 (2021), 97–117  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретный анализ и исследование операций
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