DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 22(1) (2002) 149-158
DOI: 10.7151/dmgt.1164

EDGE COLORINGS AND TOTAL COLORINGS OF INTEGER DISTANCE GRAPHS

Arnfried Kemnitz and Massimiliano Marangio

Diskrete Mathematik
Technische Universität Braunschweig
Pockelsstr. 14, D-38106 Braunschweig, Germany
e-mail: a.kemnitz@tu-bs.de
e-mail: m.marangio@tu-bs.de

Dedicated to Hansjoachim Walther on the occasion of his sixtieth birthday.

Abstract

An integer distance graph is a graph G(D) with the set Z of integers as vertex set and two vertices u,v ∈ Z are adjacent if and only if |u−v| ∈ D where the distance set D is a subset of the positive integers N. In this note we determine the chromatic index, the choice index, the total chromatic number and the total choice number of all integer distance graphs, and the choice number of special integer distance graphs.

Keywords: integer distance graph, chromatic number, choice number, chromatic index, choice index, total chromatic number, total choice number.

2000 Mathematics Subject Classification: 05C15.

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Received 22 July 2000
Revised 30 January 2001