Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports]
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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2004, Volume 1, Pages 76–90 (Mi semr7)  
This article is cited in 21 scientific papers (total in 21 papers)

Research papers

$2$-distance coloring of sparse planar graphs

O. V. Borodina, A. O. Ivanovab, T. K. Neustroevab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Yakutsk State University, Institute for Mathematics and Informatics
Full-text PDF (220 kB) Citations (21)
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Abstract: Clearly, the 2-distance chromatic number $\chi_2(G)$ of any graph $G$ with maximum degree $\Delta$ is at least $\Delta+1$. We prove that if $G$ is planar and its girth is large enough (w.r.t. a fixed $\Delta$), then $\chi_2(G)=\Delta+1$.
Received October 29, 2004, published November 16, 2004
Bibliographic databases:
Document Type: Article
UDC: 519.172.2
MSC: 05С15
Language: Russian
Citation: O. V. Borodin, A. O. Ivanova, T. K. Neustroeva, “$2$-distance coloring of sparse planar graphs”, Sib. Èlektron. Mat. Izv., 1 (2004), 76–90
Citation in format AMSBIB
\Bibitem{BorIvaNeu04}
\by O.~V.~Borodin, A.~O.~Ivanova, T.~K.~Neustroeva
\paper $2$-distance coloring of sparse planar graphs
\jour Sib. \`Elektron. Mat. Izv.
\yr 2004
\vol 1
\pages 76--90
\mathnet{http://mi.mathnet.ru/semr7}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2132449}
\zmath{https://zbmath.org/?q=an:1077.05040}
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    • This publication is cited in the following 21 articles:
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    References:70
     
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