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Durham University

Computer Science


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


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).