Clique cycle transversals in graphs with few P4's

Abstract

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 ≠ Ø 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. © 2013 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.