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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 2084–2095
DOI: https://doi.org/10.33048/semi.2020.17.139 (Mi semr1333) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Discrete mathematics and mathematical cybernetics

On perfect colorings of infinite multipath graphs

M. A. Lisitsynaa, S. V. Avgustinovichb, O. G. Parshinac

a Budyonny Military Academy of the Signal Corps, 3, pr. Tikhoretsky ave., St Petersburg, 194064, Russia
b Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
c Czech Technical University in Prague, 13, Trojanova str., Prague, 120 00, Czech Republic
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DOI: https://doi.org/10.33048/semi.2020.17.139
Abstract: A coloring of vertices of a given graph is called perfect if the color structure of each sphere of radius $1$ in the graph depends only on the color of the sphere center. Let $n$ be a positive integer. We consider a lexicographic product of the infinite path graph and a graph $G$ that can be either the complete or empty graph on $n$ vertices. We give a complete description of perfect colorings with an arbitrary number of colors of such graph products.
Keywords: perfect coloring, equitable partition, equivalent colors, infinite multipath graph.
Funding agency Grant number
Agence Nationale de la Recherche ANR-10-LABX-0070
ANR-11-IDEX-0007
Russian Foundation for Basic Research 18-31-00009
This work was performed within the framework of the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d'Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR), and has been supported by RFBS grant 18-31-00009.
Received June 11, 2020, published December 18, 2020
Bibliographic databases:
Document Type: Article
UDC: 519.174.7
MSC: 05C50
Language: English
Citation: M. A. Lisitsyna, S. V. Avgustinovich, O. G. Parshina, “On perfect colorings of infinite multipath graphs”, Sib. Èlektron. Mat. Izv., 17 (2020), 2084–2095
Citation in format AMSBIB
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\paper On perfect colorings of infinite multipath graphs
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 2084--2095
\mathnet{http://mi.mathnet.ru/semr1333}
\crossref{https://doi.org/10.33048/semi.2020.17.139}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000615617100001}
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