On cocolourings and cochromatic numbers of graphs
Discrete Applied Mathematics
Partitioning permutations into increasing and decreasing subsequences
Journal of Combinatorial Theory Series A
Partitions of graphs into one or two independent sets and cliques
Discrete Mathematics
The complexity of some problems related to Graph 3-COLORABILITY
Discrete Applied Mathematics
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
Discrete Applied Mathematics
Discrete Applied Mathematics
Two fixed-parameter algorithms for the cocoloring problem
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Partitioning extended P4-laden graphs into cliques and stable sets
Information Processing Letters
Fixed-parameter algorithms for the cocoloring problem
Discrete Applied Mathematics
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We consider the problem of partitioning the node set of a graph into p cliques and k stable sets, namely the (p,k)-coloring problem. Results have been obtained for general graphs [Feder et al., SIAM J. Discrete Math. 16 (3) (2003) 449-478], chordal graphs [Hell et al., Discrete Appl. Math. 141 (2004) 185-194] and cacti for the case where k=p in [Ekim and de Werra, On split-coloring problems, submitted for publication] where some upper and lower bounds on the optimal value minimizing k are also presented. We focus on cographs and devise some efficient algorithms for solving (p,k)-coloring problems and cocoloring problems in O(n^2+nm) time and O(n^3^/^2) time, respectively. We also give an algorithm for finding the maximum induced (p,k)-colorable subgraph. In addition to this, we present characterizations of (2,1)- and (2,2)-colorable cographs by forbidden configurations.