Chromatic number versus cochromatic number in graphs with bounded clique number
European Journal of Combinatorics
Partitions of graphs into one or two independent sets and cliques
Discrete Mathematics
P4-laden graphs: a new class of brittle graphs
Information Processing Letters
The complexity of some problems related to Graph 3-COLORABILITY
Discrete Applied Mathematics
Partitioning chordal graphs into independent sets and cliques
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
On the b-coloring of P4-tidy graphs
Discrete Applied Mathematics
Discrete Applied Mathematics
Fixed-Parameter algorithms for cochromatic number and disjoint rectangle stabbing
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Partitioning cographs into cliques and stable sets
Discrete Optimization
Fixed-parameter algorithms for the cocoloring problem
Discrete Applied Mathematics
Hi-index | 0.89 |
A (k,@?)-cocoloring of a graph is a partition of its vertex set into at most k stable sets and at most @? cliques. It is known that deciding if a graph is (k,@?)-cocolorable is NP-complete. A graph is extended P"4-laden if every induced subgraph with at most six vertices that contains more than two induced P"4@?s is {2K"2,C"4}-free. Extended P"4-laden graphs generalize cographs, P"4-sparse and P"4-tidy graphs. In this paper, we obtain a linear time algorithm to decide if, given k,@?=0, an extended P"4-laden graph is (k,@?)-cocolorable. Consequently, we obtain a polynomial time algorithm to determine the cochromatic number and the split chromatic number of an extended P"4-laden graph. Finally, we present a polynomial time algorithm to find a maximum induced (k,@?)-cocolorable subgraph of an extended P"4-laden graph, generalizing the main results of Bravo et al. (2011) [4] and Demange et al. (2005) [5].