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Chromatic numbers of integer distance graphs

โœ Scribed by Arnfried Kemnitz; Massimiliano Marangio


Book ID
108315541
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
105 KB
Volume
233
Category
Article
ISSN
0012-365X

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The distance graph G(D) with distance set D={d 1 , d 2 , ...} has the set Z of integers as vertex set, with two vertices i, j ยฅ Z adjacent if and only if |i -j| ยฅ D. We prove that the chromatic number of G(D) is finite whenever inf{d i+1 /d i } > 1 and that every growth speed smaller than this admit

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## A b&act Voigt, M. and H. Walther, On the chromatic number of special distance graphs, Discrete Mathematics 97 (1991) 395-397. For all 12 10 and u 2 1' -61+ 3 the chromatic number is proved to be 3 for distance graphs with all integers as vertices, and edges only if the vertices are at distance