Packing chromatic number of distance graphs
✍ Scribed by Jan Ekstein; Přemysl Holub; Bernard Lidický
- Book ID
- 113564743
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 514 KB
- Volume
- 160
- Category
- Article
- ISSN
- 0166-218X
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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 ¥ Z adjacent if and only if |i -j| ¥ 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
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