Let fvs(G) and cfvs(G) denote the cardinalities of a minimum feedback vertex set and a minimum connected feedback vertex set of a graph G, respectively. For a graph class G, the price of connectivity for feedback vertex set (poc-fvs) for G is defined as the maximum ratio cfvs(G)/fvs(G) over all connected graphs G in G. It is known that the poc-fvs for general graphs is unbounded. We study the poc-fvs for graph classes defined by a finite family H of forbidden induced subgraphs. We characterize exactly those finite families H for which the poc-fvs for Hfree graphs is bounded by a constant. Prior to our work, such a result was only known for the case where |H| = 1. © 2014 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Belmonte, R., Van ’T Hof, P., Kamiński, M., & Paulusma, D. (2014). Forbidden induced subgraphs and the price of connectivity for feedback vertex set. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8635 LNCS, pp. 57–68). Springer Verlag. https://doi.org/10.1007/978-3-662-44465-8_6
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