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 Β₯ Z adjacent if and only if |i -j| Β₯ 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
On embedding of finite distance graphs with large chromatic number in random graphs
β Scribed by S. V. Nagaeva; A. M. Raigorodskii
- Publisher
- Springer US
- Year
- 2009
- Tongue
- English
- Weight
- 293 KB
- Volume
- 161
- Category
- Article
- ISSN
- 1573-8795
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## Abstract An Erratum has been published for this article in Journal of Graph Theory 48: 329β330, 2005. Let __M__ be a set of positive integers. The distance graph generated by __M__, denoted by __G__(__Z, M__), has the set __Z__ of all integers as the vertex set, and edges __ij__ whenever |__i__
## 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
For each pair k, rn of natural numbers there exists a natural number f(k, rn) such that every f ( k , m)-chromatic graph contains a k-connected subgraph of chromatic number at least rn.