Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Computer Science

Profile

Publication details for Professor Matthew Johnson

Dabrowski, K.K., Johnson, M., Paesani, G., Paulusma, D. & Zamaraev, V. (2018), On the price of independence for vertex cover, feedback vertex set and odd cycle transversal, in Potapov, Igor, Spirakis, Paul & Worrell, James eds, Leibniz International Proceedings in Informatics 117: 43nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Liverpool, UK, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 63:1--63:15.

Author(s) from Durham

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).