Complexity of Grundy coloring and its variants

Edouard Bonnet (1) , Florent Foucaud (2) , Eun Jung Kim (3) , Florian Sikora (3)

1 SZTAKI - Institute for Computer Science and Control [Budapest]
2 LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

The Grundy number of a graph is the maximum number of colors used by the greedy coloring algorithm over all vertex orderings. In this paper, we study the computational complexity of Grundy Coloring, the problem of determining whether a given graph has Grundy number at least . We also study the variants Weak Grundy Coloring (where the coloring is not necessarily proper) and Connected Grundy Coloring (where at each step of the greedy coloring algorithm, the subgraph induced by the colored vertices must be connected).

Mots clés: Grundy coloring; Computational complexity; Weak Grundy; Connected Grundy; Exact algorithm; Parameterized complexity

Domaines: Informatique [cs]

Edouard Bonnet, Florent Foucaud, Eun Jung Kim, Florian Sikora. Complexity of Grundy coloring and its variants. Discrete Applied Mathematics, 2018, 243, ⟨10.1016/j.dam.2017.12.022⟩. ⟨hal-02104874⟩