Locally bounded k -colorings of trees

Cédric Bentz (1) , Christophe Picouleau (1)

1 CEDRIC - OC - CEDRIC. Optimisation Combinatoire

Given a tree T with n vertices, we show, by using a dynamic programming approach, that the problem of finding a 3-coloring of T respecting local (i.e., associated with p prespecified subsets of vertices) color bounds can be solved in O(n 6p−1 log n) time. We also show that our algorithm can be adapted to the case of k-colorings for fixed k.

Mots clés: Bounded Graph Coloring; Tree; Dynamic Programming

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Informatique [cs]

Cédric Bentz, Christophe Picouleau. Locally bounded k -colorings of trees. RAIRO - Operations Research, 2009, 43 (1), pp.27-33. ⟨10.1051/ro/2009003⟩. ⟨hal-02436823⟩