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Article Dans Une Revue Discrete Mathematics Année : 2012

b-colouring outerplanar graphs with large girth

Frédéric Maffray
Ana Silva

Résumé

A b-colouring of a graph is a colouring of its vertices such that every colour class contains a vertex that has a neighbour in all other classes. The b-chromatic number of a graph is the largest integer k such that the graph has a b-colouring with k colours. We show here how to compute in polynomial time the b-chromatic number of an outerplanar graph of girth at least 8. This generalizes the seminal result of Irving and Manlove on trees.

Dates et versions

hal-00764263 , version 1 (12-12-2012)

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Frédéric Maffray, Ana Silva. b-colouring outerplanar graphs with large girth. Discrete Mathematics, 2012, 312 (10), pp.1796-1803. ⟨10.1016/j.disc.2012.01.035⟩. ⟨hal-00764263⟩
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