On the Grundy Number of a Graph

نویسندگان

  • Frédéric Havet
  • Leonardo Sampaio
چکیده

The Grundy number of a graph G, denoted by Γ (G), is the largest k such that G has a greedy k-colouring, that is a colouring with k colours obtained by applying the greedy algorithm according to some ordering of the vertices of G. Trivially Γ (G) ≤ ∆(G) + 1. In this paper, we show that deciding if Γ (G) ≤ ∆(G) is NP-complete. We then show that deciding if Γ (G) ≥ |V (G)| − k is fixed parameter tractable with respect to the parameter k.

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تاریخ انتشار 2010