Circular chromatic numbers and fractional chromatic numbers of distance graphs

Abstract

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 D = {1, 2, . . . , m, n} with 1 ≤ m < n, for D = {q, q + 1, . . . , p} with q ≤ p, and for D = {1, 2, . . . , m} - {k} with 1 ≤ k ≤ m. © 1998 Academic Press.