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The price of connectivity for cycle transversals.

Hartinger, T.R. and Johnson, M. and Milanič, M. and Paulusma, D. (2015) 'The price of connectivity for cycle transversals.', in Mathematical foundations of computer science 2015 : 40th International Symposium, MFCS 2015, Milan, Italy, August 24-28, 2015, proceedings, part II. , pp. 395-406. Lecture notes in computer science. (9235).


For a family of graphs F, an F-transversal of a graph G is a subset S⊆V(G) that intersects every subset of V(G) that induces a subgraph isomorphic to a graph in F. Let tF(G) be the minimum size of an F-transversal of G, and ctF(G) be the minimum size of an F-transversal of G that induces a connected graph. For a class of connected graphs G, the price of connectivity for F-transversals is the supremum of the ratios ctF(G)/tF(G) over all G∈G. We perform an in-depth study into the price of connectivity for various well-known graph families F that contain an infinite number of cycles and that, in addition, may contain one or more anticycles or short paths. For each of these families we study the price of connectivity for classes of graphs characterized by one forbidden induced subgraph H. We determine exactly those classes of H-free graphs for which this graph parameter is bounded by a multiplicative constant, bounded by an additive constant, or equal to 1. In particular, our tetrachotomies extend known results of Belmonte et al. (EuroComb 2012, MFCS 2013) for the case when F is the family of all cycles.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Publisher statement:The final publication is available at Springer via
Date accepted:No date available
Date deposited:21 August 2015
Date of first online publication:August 2015
Date first made open access:11 August 2016

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