Colouring prime distance graphs

R. B. Eggleton, P. Erdös, D. K. Skilton

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

Four colours are necessary and sufficient to colour all the integers so that any two with difference equal to a prime have different colours. We investigate the corresponding problem when the set D of prescribed differences is a proper subset of the primes. In particular, we prove that if D contains {2, 3} and also contains a pair of twin primes (one of which may be 3), then four colours are necessary. Numerous results regarding periodic colourings are also obtained. However, the problem of characterizing those sets D which necessitate four colours remains open.

Original languageEnglish
Pages (from-to)17-32
Number of pages16
JournalGraphs and Combinatorics
Volume6
Issue number1
DOIs
Publication statusPublished - Mar 1 1990

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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