Chromatic numbers of integer distance graphs
โ 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
No coin nor oath required. For personal study only.
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
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
Given positive integers m, k, s with m > sk, let D m,k,s represent the set {1, 2, . . . , m}\{k, 2k, . . . , sk}. The distance graph G(Z , D m,k,s ) has as vertex set all integers Z and edges connecting i and j whenever |i -j| โ D m,k,s . This paper investigates chromatic numbers and circular chroma
## 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