On the price of independence for vertex cover, feedback vertex set and odd cycle transversal

Dabrowski, K. K.; Johnson, M.; Paesani, G.; Paulusma, D.; Zamaraev, V.

Abstract

Let vc(G), fvs(G) and oct(G) denote, respectively, the size of a minimum vertex cover, minimum feedback vertex set and minimum odd cycle transversal in a graph G. One can ask, when looking for these sets in a graph, how much bigger might they be if we require that they are independent; that is, what is the price of independence? If G has a vertex cover, feedback vertex set or odd cycle transversal that is an independent set, then we let, respectively, ivc(G), ifvs(G) or ioct(G) denote the minimum size of such a set. We investigate for which graphs H the values of ivc(G), ifvs(G) and ioct(G) are bounded in terms of vc(G), fvs(G) and oct(G), respectively, when the graph G belongs to the class of H-free graphs. We find complete classifications for vertex cover and feedback vertex set and an almost complete classification for odd cycle transversal (subject to three non-equivalent open cases).

Citation

Dabrowski, K. K., Johnson, M., Paesani, G., Paulusma, D., & Zamaraev, V. (2018, August). On the price of independence for vertex cover, feedback vertex set and odd cycle transversal. Presented at 43nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)., Liverpool, UK

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 43nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018).
• Start Date: Aug 27, 2018
• End Date: Aug 31, 2018
• Acceptance Date: Jun 25, 2018
• Publication Date: Jan 1, 2018
• Deposit Date: Jul 30, 2018
• Publicly Available Date: Jun 27, 2019
• Peer Reviewed: Peer Reviewed
• Pages: 63:1-63:15
• Series Title: Leibniz International Proceedings in Informatics
• Series Number: 117
• Series ISSN: 1868-8969
• Book Title: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018).
• DOI: https://doi.org/10.4230/lipics.mfcs.2018.63
• Public URL: https://durham-repository.worktribe.com/output/1145032