✦ LIBER ✦

On the chromatic number of special distance graphs

✍ Scribed by M. Voigt; H. Walther

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 153 KB
Volume: 97
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90454-a

No coin nor oath required. For personal study only.

✦ Synopsis

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 distances 2,3, u, and u + 1.

📜 SIMILAR VOLUMES

Distance Graphs with Finite Chromatic Nu

Distance Graphs with Finite Chromatic Number

✍ I.Z. Ruzsa; Zs. Tuza; M. Voigt 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 96 KB

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

Circular Chromatic Numbers and Fractiona

Circular Chromatic Numbers and Fractional Chromatic Numbers of Distance Graphs

✍ G.J. Chang; L. Huang; X. Zhu 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 171 KB

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

Circular chromatic number of distance gr

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

✍ Xuding Zhu 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 104 KB

## Abstract Suppose __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 gra

Circular Chromatic Numbers of Distance G

Circular Chromatic Numbers of Distance Graphs with Distance Sets Missing Multiples

✍ Lingling Huang; Gerard J Chang 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 114 KB

Given positive integers m, k, s with m > sk, 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 . This paper investigates chromatic numbers and circular chroma

Fractional chromatic number and circular

Fractional chromatic number and circular chromatic number for distance graphs with large clique size

✍ Daphne Der-Fen Liu; Xuding Zhu 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 136 KB

## Abstract An Erratum has been published for this article in Journal of Graph Theory 48: 329–330, 2005. Let __M__ be a set of positive integers. The distance graph generated by __M__, denoted by __G__(__Z, M__), has the set __Z__ of all integers as the vertex set, and edges __ij__ whenever |__i__

On the chromatic number of disk graphs

✍ Malesi?ska, Ewa; Piskorz, Steffen; Wei�enfels, Gerhard 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 172 KB 👁 2 views

Colorings of disk graphs arise in the study of the frequency-assignment problem in broadcast networks. Motivated by the observations that the chromatic number of graphs modeling real networks hardly exceeds their clique number, we examine the related properties of the unit disk (UD) graphs and their