On edge-b-critical graphs

Mostafa Blidia (1) , Noureddine Ikhlef-Eschouf (1) , Frédéric Maffray (2)

1 UB1 - Université Saâd Dahlab Blida 1
2 G-SCOP_OC - Optimisation Combinatoire

A b-coloring of a graph G is a proper coloring of the vertices of G such that in each color class there exists a vertex having neighbors inall the other color classes. The b-chromatic number b(G) of a graph G isthe largest integer such that G admits a b-coloring with k colors. Agraph G is edge b-critical if deleting any edge decreases its b-chromaticnumber. We characterize the class of P5-free graphs, d-regular graphsand trees which are edge b-critical. As a consequence we show that decidingif a graph is edge-b-critical is NP-hard.

Mots clés: edge b-critical graph; b-chromatic number; b-coloring

Domaines: Mathématique discrète [cs.DM]

Mostafa Blidia, Noureddine Ikhlef-Eschouf, Frédéric Maffray. On edge-b-critical graphs. Discrete Applied Mathematics, 2015, 180, pp.176-180. ⟨10.1016/j.dam.2014.08.012⟩. ⟨hal-01212153⟩