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Contemporary Mathematics. Fundamental Directions, 2013, Volume 51, Pages 64–73 (Mi cmfd254)  
This article is cited in 1 scientific paper (total in 1 paper)

On large subgraphs with small chromatic numbers contained in distance graphs

A. A. Kokotkin, A. M. Raigorodskii

Dolgoprudnyi, Moscow region, Russia
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Abstract: It is proved that each distance graph on a plane has an induced subgraph with a chromatic number that is at most 4 containing over 91 % of the vertices of the original graph. This result is used to obtain the asymptotic growth rate for a threshold probability that a random graph is isomorphic to a certain distance graph on a plane. Several generalizations to larger dimensions are proposed.
English version:
Journal of Mathematical Sciences, 2016, Volume 214, Issue 5, Pages 665–674
DOI: https://doi.org/10.1007/s10958-016-2804-3
Document Type: Article
UDC: 519.174
Language: Russian
Citation: A. A. Kokotkin, A. M. Raigorodskii, “On large subgraphs with small chromatic numbers contained in distance graphs”, Topology, CMFD, 51, PFUR, M., 2013, 64–73; Journal of Mathematical Sciences, 214:5 (2016), 665–674
Citation in format AMSBIB
\Bibitem{KokRai13}
\by A.~A.~Kokotkin, A.~M.~Raigorodskii
\paper On large subgraphs with small chromatic numbers contained in distance graphs
\inbook Topology
\serial CMFD
\yr 2013
\vol 51
\pages 64--73
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd254}
\transl
\jour Journal of Mathematical Sciences
\yr 2016
\vol 214
\issue 5
\pages 665--674
\crossref{https://doi.org/10.1007/s10958-016-2804-3}
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