Raquel Bravo ; Sulamita Klein ; Loana Tito Nogueira ; Fábio Protti - Clique cycle transversals in graphs with few P₄'s

dmtcs:616 - Discrete Mathematics & Theoretical Computer Science, September 26, 2013, Vol. 15 no. 3 - https://doi.org/10.46298/dmtcs.616
Clique cycle transversals in graphs with few P₄'sArticle

Authors: Raquel Bravo 1; Sulamita Klein 2; Loana Tito Nogueira 1; Fábio Protti 1

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.

Volume: Vol. 15 no. 3
Section: Graph Theory
Published on: September 26, 2013
Accepted on: June 9, 2015
Submitted on: September 26, 2012
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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