Forbidden Induced Subgraphs and the Price of Connectivity for Feedback Vertex Set
نویسندگان
چکیده
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.
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