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 the b-continuity property of graphs
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
Notes: On approximating the b-chromatic number
Discrete Applied Mathematics
On the b-dominating coloring of graphs
Discrete Applied Mathematics
The b-Chromatic Number of Cubic Graphs
Graphs and Combinatorics
On the b-coloring of P4-tidy graphs
Discrete Applied Mathematics
Bounds for the b-chromatic number of G-v
Discrete Applied Mathematics
| Hi-index | 0.04 |
The b-chromatic number of a graph G, denoted by @f(G), is the largest integer k for which G admits a proper coloring by k colors, such that each color class has a vertex that is adjacent to at least one vertex in each of the other color classes. We prove that, for each d-regular graph G which contains no 4-cycle, @f(G)=@?d+32@?; and besides, if G has a triangle, then @f(G)=@?d+42@?. Also, if G is a d-regular graph that contains no 4-cycle and diam(G)=6, then @f(G)=d+1. Finally, we show that, for any d-regular graph G which does not contain 4-cycle and has vertex connectivity less than or equal to d+12, @f(G)=d+1. Moreover, when the vertex connectivity is less than 3d-34, we introduce a lower bound for the b-chromatic number in terms of the vertex connectivity.