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Distance graphs with missing multiples in the distance sets

✍ Scribed by Liu, Daphne D.-F.; Zhu, Xuding

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
141 KB
Volume
30
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Given positive integers m, k, and s with m > ks, 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| ∈ D m,k,s . The chromatic number and the fractional chromatic number of G(Z, D m,k,s ) are denoted by Ο‡(Z, D m,k,s ) and Ο‡ f (Z, D m,k,s ), respectively. For s = 1, Ο‡(Z, D m,k,1 ) was studied by Eggleton, ErdΕ‘s, and Skilton [6], Kemnitz and Kolberg [12], and Liu [13], and was solved lately by

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