Article Dans Une Revue Discrete Mathematics Année : 2014

On the family of r-regular graphs with Grundy number r+1

Résumé

The Grundy number of a graph G, denoted by Γ(G), is the largest k such that there exists a partition of V(G), into k independent sets V1,,Vk and every vertex of Vi is adjacent to at least one vertex in Vj, for every j<i. The objects which are studied in this article are families of r-regular graphs such that Γ(G)=r+1. Using the notion of independent module, a characterization of this family is given for r=3. Moreover, we determine classes of graphs in this family, in particular the class of r-regular graphs without induced C4, for r4. Furthermore, our propositions imply results on partial Grundy number.
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Dates et versions

hal-00922022 , version 1 (23-12-2013)
hal-00922022 , version 2 (19-05-2014)

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Citer

Nicolas Gastineau, Hamamache Kheddouci, Olivier Togni. On the family of r-regular graphs with Grundy number r+1. Discrete Mathematics, 2014, 328 (5-15), pp.5-15. ⟨10.1016/j.disc.2014.03.023⟩. ⟨hal-00922022v2⟩
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