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
Chromatic number of prime distance graphs
โ Scribed by M. Voigt; H. Walther
- Book ID
- 104183154
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 619 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0166-218X
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๐ SIMILAR VOLUMES
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
## 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
## Abstract Suppose __D__ is a subset of __R__^+^. The distance graph __G__(__R, D__) is the graph with vertex set __R__ in which two vertices __x__,__y__ are adjacent if |__x__โ__y__| โ __D__. This study investigates the circular chromatic number and the fractional chromatic number of distance gra