On the Grundy number of graphs with few P4's - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Applied Mathematics Year : 2012

On the Grundy number of graphs with few P4's


The Grundy number of a graph G is the largest number of colors used by any execution of the greedy algorithm to color G. The problem of determining the Grundy number of G is polynomial if G is a P4-free graph and NP-hard if G is a P5-free graph. In this article, we define a new class of graphs, the fat-extended P4-laden graphs, and we show a polynomial time algorithm to determine the Grundy number of any graph in this class. Our class intersects the class of P5-free graphs and strictly contains the class of P4-free graphs. More precisely, our result implies that the Grundy number can be computed in polynomial time for any graph of the following classes: P4-reducible, extended P4-reducible, P4-sparse, extended P4-sparse, P4-extendible, P4-lite, P4-tidy, P4-laden and extended P4-laden, which are all strictly contained in the fat-extended P4-laden class.
Fichier principal
Vignette du fichier
grundy_p4-full-withmodifs.pdf (212.91 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00639008 , version 1 (07-11-2011)



Julio Araujo, Claudia Linhares Sales. On the Grundy number of graphs with few P4's. Discrete Applied Mathematics, 2012, 160 (18), pp.2514-2522. ⟨10.1016/j.dam.2011.08.016⟩. ⟨inria-00639008⟩
320 View
176 Download



Gmail Facebook X LinkedIn More