Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903524 | Electronic Notes in Discrete Mathematics | 2017 | 6 Pages |
Abstract
A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to each other color class. The b-chromatic number of G is the maximum integer Ïb(G) for which G has a b-coloring with Ïb(G) colors. A graph G is b-continuous if G has a b-coloring with k colors, for every integer k in the interval [Ï(G),Ïb(G)]. It is known that not all graphs are b-continuous, and also that the cartesian product and the strong product do not preserve b-continuity. However, the same is not known to be true about the lexicographic product G[H]. Here, we prove that G[H] is b-continuous whenever H is b-continuous and G is an interval graph, a block graph or a cograph.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Cláudia Linhares Sales, Leonardo Sampaio, Ana Silva,