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Forbidden induced subgraphs and the price of connectivity for feedback vertex set.

Belmonte, R. and Hof, van 't P. and Kaminski, M. and Paulusma, D. (2014) 'Forbidden induced subgraphs and the price of connectivity for feedback vertex set.', in 39th International Symposium, MFCS 2014, Budapest, Hungary, 26-29 August 2014 ; proceedings, Part II. Berlin, Heidelberg: Springer, pp. 57-68. Lecture notes in computer science. (8635).


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 H-free graphs is bounded by a constant. Prior to our work, such a result was only known for the case where |H|=1.

Item Type:Book chapter
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Date accepted:No date available
Date deposited:16 January 2015
Date of first online publication:2014
Date first made open access:No date available

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