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Diskretnyi Analiz i Issledovanie Operatsii, 2022, Volume 29, Issue 1, Pages 33–45
DOI: https://doi.org/10.33048/daio.2022.29.718 (Mi da1291) 		 
On perfect colorings of paths divisible by a matching

M. A. Lisitsynaa, S. V. Avgustinovichb

a Budyonny Military Academy of the Signal Corps, 3 Tikhoretsky Avenue, 194064 St. Petersburg, Russia
b Sobolev Institute of Mathematics, 4 Koptyug Avenue, 630090 Novosibirsk, Russia
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DOI: https://doi.org/10.33048/daio.2022.29.718
Abstract: A vertex coloring of a graph $G$ is called perfect if the color structure of the neighborhood of each vertex depends only on the color of this vertex. We give a complete characterization of perfect colorings with an arbitrary number of colors of the lexicographic product of the infinite path graph and the matching. Illustr. 1, bibliogr. 18.
Keywords: perfect coloring, equitable partition, infinite path graph, matching, lexicographic product.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0017
This research was carried out within the framework of the state contract for Sobolev Institute of Mathematics, project no. 0314-2019-0016.
Received: 07.06.2021
Revised: 08.11.2021
Accepted: 29.11.2021
English version:
Journal of Applied and Industrial Mathematics, 2022, Volume 16, Issue 1, Pages 98–104
DOI: https://doi.org/10.1134/S1990478922010094
Bibliographic databases:
Document Type: Article
UDC: 519.174.7
Language: Russian
Citation: M. A. Lisitsyna, S. V. Avgustinovich, “On perfect colorings of paths divisible by a matching”, Diskretn. Anal. Issled. Oper., 29:1 (2022), 33–45; J. Appl. Industr. Math., 16:1 (2022), 98–104
Citation in format AMSBIB
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\by M.~A.~Lisitsyna, S.~V.~Avgustinovich
\paper On perfect colorings of paths divisible~by~a~matching
\jour Diskretn. Anal. Issled. Oper.
\yr 2022
\vol 29
\issue 1
\pages 33--45
\mathnet{http://mi.mathnet.ru/da1291}
\crossref{https://doi.org/10.33048/daio.2022.29.718}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4412507}
\transl
\jour J. Appl. Industr. Math.
\yr 2022
\vol 16
\issue 1
\pages 98--104
\crossref{https://doi.org/10.1134/S1990478922010094}
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