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1 Department of Physics and Computer Science Waterloo 2 G-SCOP OC - OC G-SCOP - Laboratoire des sciences pour la conception, l-optimisation et la production 3 Laboratoire LAID3

Abstract : A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b-chromatic number of a graph G is the largest integer k such that G admits a b-coloring with k colors. A graph is b-perfect if the b-chromatic number is equal to the chromatic number for every induced subgraph of G. We prove that a graph is b-perfect if and only if it does not contain as an induced subgraph a member of a certain list of twenty-two graphs. This entails the existence of a polynomial-time recognition algorithm and of a polynomial-time algorithm for coloring exactly the vertices of every b-perfect graph.





Autor: Chinh Hoàng - Frédéric Maffray - Meriem Mechebbek -

Fuente: https://hal.archives-ouvertes.fr/



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