(p, k)-coloring problems in line graphs

Authors:
Marc Demange;Tinaz Ekim;Dominique de Werra
Affiliations:
ESSEC, Département SID, France;EPFL, Recherche Opérationnelle Sud Est (ROSE), Switzerland;EPFL, Recherche Opérationnelle Sud Est (ROSE), Switzerland
Venue:
Theoretical Computer Science
Year:
2005

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Abstract

The (p, k)-coloring problems generalize the usual coloring problem by replacing stable sets by cliques and stable sets. Complexities of some variations of (p, k)-coloring problems (split-coloring and cocoloring) are studied in line graphs; polynomial algorithms or proofs of NP-completeness are given according to the complexity status. We show that the most general (p, k)-coloring problems are more difficult than the cocoloring and the split-coloring problems while there is no such relation between the last two problems. We also give complexity results for the problem of finding a maximum (p, k)-colorable subgraph in line graphs. Finally, upper bounds on the optimal values are derived in general graphs by sequential algorithms based on Welsh-Powell and Matula orderings.