A graph is extended P4-laden if each of its induced subgraphs with at most six vertices that contains more than two induced P4's is 2K2,C4-free. A cycle transversal (or feedback vertex set) of a graph G is a subset T ⊆ V (G) such that T ∩ V (C) 6= ∅ for every cycle C of G; if, in addition, T is a clique, then T is a clique cycle transversal (cct). Finding a cct in a graph G is equivalent to partitioning V (G) into subsets C and F such that C induces a complete subgraph and F an acyclic subgraph. This work considers the problem of characterizing extended P4-laden graphs admitting a cct. We characterize such graphs by means of a finite family of forbidden induced subgraphs, and present a linear-time algorithm to recognize them.

Source : oai:HAL:hal-00966377v1

Volume: Vol. 15 no. 3

Section: Graph Theory

Published on: September 26, 2013

Submitted on: September 26, 2012

Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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