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Pré-Publication, Document De Travail Année : 2013

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

Olivier Togni

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 in Vi is adjacent to at least one vertex in Vj , for every j < i. We consider the following question for which we give some partial answers: Does the equality Γ(G) = r + 1 hold for any r-regular graph without induced 4-cycle?
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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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Nicolas Gastineau, Hamamache Kheddouci, Olivier Togni. On the family of r-regular graphs with Grundy number r + 1. 2013. ⟨hal-00922022v1⟩
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