Regular Article: Bi-complement Reducible Graphs
Advances in Applied Mathematics
The b-chromatic number of a graph
Discrete Applied Mathematics
Some bounds for the b-chromatic number of a graph
Discrete Mathematics
On a Generalization of Bi-Complement Reducible Graphs
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
On the b-Chromatic Number of Graphs
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
On b-colorings in regular graphs
Discrete Applied Mathematics
On the b-dominating coloring of graphs
Discrete Applied Mathematics
The b-Chromatic Number of Cubic Graphs
Graphs and Combinatorics
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A b-coloring of a graph G by k colors is a proper vertex coloring such that every color class contains a color-dominating vertex, that is, a vertex having neighbors in all other k-1 color classes. The b-chromatic number @g"b(G) is the maximum integer k for which G has a b-coloring by k colors. For a bipartite graph G=(A@?B,E), the bicomplement of G is the bipartite graph G@?=(A@?B,E@?) with E@?:={{a,b}|a@?A,b@?B,{a,b}@?E}. In this paper, we investigate the b-chromatic number for bipartite graphs with a special bicomplement. In particular, we consider graphs G for which G@? is disconnected or has maximum degree @D(G@?)@?2. Moreover, we give partial answers to the question ''Which d-regular bipartite graphs G satisfy @g"b(G)=d+1?'' and we show a Nordhaus-Gaddum-type result for G and G@?.