Chromatic number versus cochromatic number in graphs with bounded clique number
European Journal of Combinatorics
A tree representation for P4-sparse graphs
Discrete Applied Mathematics
Partitions of graphs into one or two independent sets and cliques
Discrete Mathematics
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
On the structure of graphs with few P4s
Discrete Applied Mathematics
Complexity of graph partition problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximating minimum cocolorings
Information Processing Letters
SIAM Journal on Discrete Mathematics
Partitioning chordal graphs into independent sets and cliques
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
(p, k)-coloring problems in line graphs
Theoretical Computer Science
Graph Theory
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
Partitioning extended P4-laden graphs into cliques and stable sets
Information Processing Letters
| Hi-index | 0.04 |
A (k,@?)-cocoloring of a graph G is a partition of the vertex set of G into at most k independent sets and at most @? cliques. It is known that determining the cochromatic number and the split chromatic number, which are respectively the minimum k+@? and the minimum max{k,@?} such that G is (k,@?)-cocolorable, is NP-hard problem. A (q,q-4)-graph is a graph such that every subset of at most q vertices induces at most q-4 distinct P"4's. In 2011, Bravo et al. obtained a polynomial time algorithm to decide if a (5,1)-graph is (k,@?)-cocolorable (Bravo et al., 2011). In this paper, we extend this result by obtaining polynomial time algorithms to decide the (k,@?)-cocolorability and to determine the cochromatic number and the split chromatic number for (q,q-4)-graphs for every fixed q and for graphs with bounded treewidth. We also obtain a polynomial time algorithm to obtain the maximum (k,@?)-cocolorable subgraph of a (q,q-4)-graph for every fixed q. All these algorithms are fixed parameter tractable.