The price of connectivity for cycle transversals

Hartinger, T.R.; Johnson, M.; Milanič, M.; Paulusma, D.

doi:10.1007/978-3-662-48054-0_33

The price of connectivity for cycle transversals

Hartinger, T.R.; Johnson, M.; Milanič, M.; Paulusma, D.

Authors

T.R. Hartinger

Professor Matthew Johnson matthew.johnson2@durham.ac.uk
Head Of Department

M. Milanič

Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor

Abstract

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.

Citation

Hartinger, T., Johnson, M., Milanič, M., & 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 (395-406). https://doi.org/10.1007/978-3-662-48054-0_33

Conference Name	40th International Symposium, MFCS 2015
Conference Location	Milan, Italy
Publication Date	Aug 11, 2015
Deposit Date	Aug 12, 2015
Publicly Available Date	Aug 11, 2016
Pages	395-406
Series Title	Lecture notes in computer science
Series Number	9235
Series ISSN	0302-9743,1611-3349
Book Title	Mathematical foundations of computer science 2015 : 40th International Symposium, MFCS 2015, Milan, Italy, August 24-28, 2015, proceedings, part II.
ISBN	9783662480533
DOI	https://doi.org/10.1007/978-3-662-48054-0_33
Additional Information	Conference dates: August 24-28, 2015