Vertex colorings with a distance restriction

Guantao Chen, A. Gyárfás, R. H. Schelp

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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
Volume191
Issue number1-3
Publication statusPublished - Sep 28 1998

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Vertex Coloring
Coloring
Restriction
Color
Graph in graph theory
Colouring
Integer

Keywords

  • Chromatic number
  • Coloring
  • Distance
  • Extremal number

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Chen, G., Gyárfás, A., & Schelp, R. H. (1998). Vertex colorings with a distance restriction. Discrete Mathematics, 191(1-3), 65-82.

Vertex colorings with a distance restriction. / Chen, Guantao; Gyárfás, A.; Schelp, R. H.

In: Discrete Mathematics, Vol. 191, No. 1-3, 28.09.1998, p. 65-82.

Research output: Contribution to journalArticle

Chen, G, Gyárfás, A & Schelp, RH 1998, 'Vertex colorings with a distance restriction', Discrete Mathematics, vol. 191, no. 1-3, pp. 65-82.
Chen, Guantao ; Gyárfás, A. ; Schelp, R. H. / Vertex colorings with a distance restriction. In: Discrete Mathematics. 1998 ; Vol. 191, No. 1-3. pp. 65-82.
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