Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10118320 | European Journal of Combinatorics | 2005 | 14 Pages |
Abstract
Let D be a set of positive integers. The distance graph G(Z,D) with distance set D is the graph with vertex set Z in which two vertices x,y are adjacent if and only if |xây|âD. The fractional chromatic number, the chromatic number, and the circular chromatic number of G(Z,D) for various D have been extensively studied recently. In this paper, we investigate the fractional chromatic number, the chromatic number, and the circular chromatic number of the distance graphs with the distance sets of the form Dm,[k,kâ²]={1,2,â¦,m}â{k,k+1,â¦,kâ²}, where m, k, and kâ² are natural numbers with mâ¥kâ²â¥k. In particular, we completely determine the chromatic number of G(Z,Dm,[2,kâ²]) for arbitrary m, and kâ².
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Peter Che Bor Lam, Wensong Lin,