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26 April 2024

» arxiv » 1202.2968

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Distance graphs having large chromatic numbers and not containing cliques or cycles of given size
Evgeniy Demekhin ; Andrei Raigorodskii ; Oleg Rubanov ;
Date:	14 Feb 2012
Abstract:	In this work, the classical Nelson -- Hadwiger problem is studied which lies on the edge of combinatorial geometry and graph theory. It concerns colorings of distance graphs in $ {mathbb R}^n $, i.e., graphs such that their vertices are vectors and their edges are pairs of vectors at a distance from a given set of postive numbers apart. A series of new lower bounds are obtained for the chromatic numbers of such graphs with different restrictions on the clique numbers and the girths.
Source:	arXiv, 1202.2968
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