Characterization and recognition of P4-sparse graphs partitionable into k independent sets and ℓ cliques

Authors:
Raquel S. F. Bravo;Sulamita Klein;Loana Tito Nogueira;FáBio Protti
Affiliations:
COPPE-PESC, Universidade Federal do Rio de Janeiro, Brazil;COPPE-PESC, Universidade Federal do Rio de Janeiro, Brazil;IC, Universidade Federal Fluminense, Brazil;IC, Universidade Federal Fluminense, Brazil
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

In this work, we focus on the class of P"4-sparse graphs, which generalizes the well-known class of cographs. We consider the problem of verifying whether a P"4-sparse graph is a (k,@?)-graph, that is, a graph that can be partitioned into k independent sets and @? cliques. First, we describe in detail the family of forbidden induced subgraphs for a cograph to be a (k,@?)-graph. Next, we show that the same forbidden structures suffice to characterize P"4-sparse graphs which are (k,@?)-graphs. Finally, we describe how to recognize (k,@?)-P"4-sparse graphs in linear time by using special auxiliary cographs.