The b-chromatic number of a graph
Discrete Applied Mathematics
Some bounds for the b-chromatic number of a graph
Discrete Mathematics
On the b-Chromatic Number of Graphs
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
On approximating the b-chromatic number
Discrete Applied Mathematics
On b-colorings in regular graphs
Discrete Applied Mathematics
On the b-Coloring of Cographs and P 4-Sparse Graphs
Graphs and Combinatorics
Note: On the b-chromatic number of Kneser graphs
Discrete Applied Mathematics
On the b-dominating coloring of graphs
Discrete Applied Mathematics
The b-Chromatic Number of Cubic Graphs
Graphs and Combinatorics
| Hi-index | 0.04 |
A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. The b-spectrum S"b(G) of a graph G is the set of positive integers k,@g(G)@?k@?b(G), for which G has a b-coloring using k colors. A graph G is b-continuous if S"b(G) = the closed interval [@g(G),b(G)]. In this paper, we obtain an upper bound for the b-chromatic number of some families of Kneser graphs. In addition we establish that [@g(G),n+k+1]@?S"b(G) for the Kneser graph G=K(2n+k,n) whenever 3@?n@?k+1. We also establish the b-continuity of some families of regular graphs which include the family of odd graphs.