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arXiv · 1904.01600

New bounds for the b-chromatic number of vertex deleted graphs

Renata Del-Vecchio·Mekkia Kouider
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Abstract

A b-coloring of a graph is a proper coloring of its vertices such that each color class contains a vertex adjacent to at least one vertex of every other color class. The b-chromatic number of a graph is the largest integer k such that the graph has a b-coloring with k colors. In this work we present lower bounds for the b-chromatic number of a vertex-deleted subgraph of a graph, particularly regarding two important classes, quasi-line and chordal graphs. We also get bounds for the b-chromatic number of G -{x}, when G is a graph with large girth.

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Renata Del-Vecchio, Mekkia Kouider. 2019-04-02. New bounds for the b-chromatic number of vertex deleted graphs. https://arxiv.org/abs/1904.01600

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