Distant Vertex Partitions of Graphs

  • Authors:

  • Chris Jagger

  • Affiliations:

  • Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB, England (e-mail: C.N.Jagger@dpmms.cam.ac.uk)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 1998

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Abstract

We consider the function χ(Gk), defined to be the smallest number of colours that can colour a graph G in such a way that no vertices of distance at most k receive the same colour. In particular we shall look at how small a value this function can take in terms of the order and diameter of G. We get general bounds for this and tight bounds for the cases k=2 and k=3.