Connectedness of Strong k-Colour Graphs

Somkiat Trakultraipruk

Connectedness of Strong k-Colour Graphs

Combinatorics 2010-09-23 v1

Authors: Somkiat Trakultraipruk

Abstract

For a positive integer k and a graph G, we consider proper vertex-colourings of G with k colours in which all k colours are actually used. We call such a colouring a strong k-colouring. The strong k-colour graph of G, S_k(G), is the graph that has all the strong k-colourings of G as its vertex set, and two colourings are adjacent in S_k(G) if they differ in colour on only one vertex of G. In this paper, we show some results related to the question : For what G and k is S_k(G) connected ?

Keywords

rainbow connection graph coloring graph theory

Cite

@article{arxiv.1009.4440,
  title  = {Connectedness of Strong k-Colour Graphs},
  author = {Somkiat Trakultraipruk},
  journal= {arXiv preprint arXiv:1009.4440},
  year   = {2010}
}

Comments

15 pages

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