Vertex colorings with a distance restriction

Guantao Chen, András Gyárfás, R. H. Schelp

Research output: Contribution to journalArticle

6 Citations (Scopus)


Let d, k be any two positive integers with k > d > 0. We consider a k-coloring of a graph G such that the distance between each pair of vertices in the same color-class is at least d. Such graphs are said to be (k,d)-colorable. The object of this paper is to determine the maximum size of (k,3)-colorable, (k,4)-colorable, and (k,k-1)-colorable graphs. Sharp results are obtained for both (k,3)-colorable and (k,k-1)-colorable graphs, while the results obtained for (k,4)-colorable graphs are close to the truth.

Original languageEnglish
Pages (from-to)65-82
Number of pages18
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - Sep 28 1998


  • Chromatic number
  • Coloring
  • Distance
  • Extremal number

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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