Distance graphs with finite chromatic number

I. Z. Ruzsa, Zs Tuza, M. Voigt

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

The distance graph G(D) with distance set D = {d1, d2,...} 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{di+1/di} > 1 and that every growth speed smaller than this admits a distance set D with infinite-chromatic G(D).

Original languageEnglish
Pages (from-to)181-187
Number of pages7
JournalJournal of Combinatorial Theory. Series B
Volume85
Issue number1
DOIs
Publication statusPublished - Jan 1 2002

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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