Distance graphs with large chromatic numbers and small clique numbers
โ Scribed by A. B. Kupavskii, A. M. Raigorodskii
- Book ID
- 114993294
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 2012
- Tongue
- English
- Weight
- 232 KB
- Volume
- 85
- Category
- Article
- ISSN
- 1064-5624
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## Abstract An Erratum has been published for this article in Journal of Graph Theory 48: 329โ330, 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__
This paper studies circular chromatic numbers and fractional chromatic numbers of distance graphs G(Z , D) for various distance sets D. In particular, we determine these numbers for those D sets of size two, for some special D sets of size three, for
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