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

Belmonte, R.; Hof, van 't P.; Kaminski, M.; Paulusma, D.

Abstract

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.

Citation

Belmonte, R., Hof, V. '. P., Kaminski, M., & Paulusma, D. (2014, December). Forbidden Induced Subgraphs and the Price of Connectivity for Feedback Vertex Set. Presented at 39th International Symposium, MFCS 2014, Budapest, Hungary

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 39th International Symposium, MFCS 2014
• Publication Date: Jan 1, 2014
• Deposit Date: Dec 20, 2014
• Publicly Available Date: Jan 16, 2015
• Print ISSN: 0302-9743
• Pages: 57-68
• Series Title: Lecture notes in computer science
• Series Number: 8635
• Series ISSN: 0302-9743,1611-3349
• Book Title: 39th International Symposium, MFCS 2014, Budapest, Hungary, 26-29 August 2014 ; proceedings, Part II.
• ISBN: 9783662444641
• DOI: https://doi.org/10.1007/978-3-662-44465-8_6
• Public URL: https://durham-repository.worktribe.com/output/1154514