On a unique tree representation for P4-extendible graphs
Discrete Applied Mathematics - Special volume: combinatorics and theoretical computer science
P-Components and the Homogeneous Decomposition of Graphs
SIAM Journal on Discrete Mathematics
On the structure of graphs with few P4s
Discrete Applied Mathematics
The b-chromatic number of a graph
Discrete Applied 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 the b-dominating coloring of graphs
Discrete Applied Mathematics
On the b-Coloring of Cographs and P 4-Sparse Graphs
Graphs and Combinatorics
On minimally b-imperfect graphs
Discrete Applied Mathematics
The b-Chromatic Number of Cubic Graphs
Graphs and Combinatorics
On the b-chromatic number of regular graphs without 4-cycle
Discrete Applied Mathematics
Partitioning extended P4-laden graphs into cliques and stable sets
Information Processing Letters
Hi-index | 0.04 |
A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by @g"b(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every t=@g(G),...,@g"b(G), and it is b-monotonic if @g"b(H"1)=@g"b(H"2) for every induced subgraph H"1 of G, and every induced subgraph H"2 of H"1. In this work, we prove that P"4-tidy graphs (a generalization of many classes of graphs with few induced P"4s) are b-continuous and b-monotonic. Furthermore, we describe a polynomial time algorithm to compute theb-chromatic number for this class of graphs.