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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= ∅ 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.
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Raquel Bravo, Sulamita Klein, Loana Tito Nogueira, Fábio Protti. Clique cycle transversals in graphs with few P₄'s. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 3 (3), pp.13--20. ⟨10.46298/dmtcs.616⟩. ⟨hal-00966377⟩

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