The price of connectivity for cycle transversals

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

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, August). The price of connectivity for cycle transversals. Presented at 40th International Symposium, MFCS 2015, Milan, Italy

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 40th International Symposium, MFCS 2015
• Publication Date: Aug 11, 2015
• Deposit Date: Aug 12, 2015
• Publicly Available Date: Aug 11, 2016
• Print ISSN: 0302-9743
• 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
• Public URL: https://durham-repository.worktribe.com/output/1153166
• Additional Information: Conference dates: August 24-28, 2015