Circular chromatic number of distance graphs with distance sets of cardinality 3

Abstract

AbstractSuppose 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−y| ∈ D. This study investigates the circular chromatic number and the fractional chromatic number of distance graphs G(R,D) with |D| = 3. As a consequence, we determine the chromatic numbers of all such distance graphs. This settles a conjecture proposed independently by Chen et al. [J. Chen, G. Chang, and K. Huang, J Graph Theory 25 (1997) 281–287 and Voigt [M. Voigt Ars Combinatoria, 52 (1999) 3–12] in the affirmative. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 195–207, 2002