Coloring Artemis graphs

Benjamin Lévêque (1) , Frédéric Maffray (1) , Bruce Reed , Nicolas Trotignon (2)

1 G-SCOP_OC - Optimisation Combinatoire
2 Leibniz - IMAG - Laboratoire Leibniz

We consider the class A of graphs that contain no odd hole, no antihole, and no "prism" (a graph consisting of two disjoint triangles with three disjoint paths between them). We show that the coloring algorithm found by the second and fourth author can be implemented in time O(n^2m) for any graph in A with n vertices and m edges, thereby improving on the complexity proposed in the original paper.

Mots clés: Coloring; Algorithm; Perfect graphs; Artemis graphs

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Benjamin Lévêque, Frédéric Maffray, Bruce Reed, Nicolas Trotignon. Coloring Artemis graphs. Theoretical Computer Science, 2009, 410, pp.2234-2240. ⟨10.1016/j.tcs.2009.02.012⟩. ⟨hal-00004741⟩