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On the Price of Independence for Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal

Authors Konrad K. Dabrowski , Matthew Johnson , Giacomo Paesani , Daniël Paulusma , Viktor Zamaraev

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
Keywords
  • vertex cover
  • feedback vertex set
  • odd cycle transversal
  • price of independence

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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).

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Konrad K. Dabrowski, Matthew Johnson, Giacomo Paesani, Daniël Paulusma, and Viktor Zamaraev. On the Price of Independence for Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 63:1-63:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.MFCS.2018.63

Author Details

Konrad K. Dabrowski
  • Department of Computer Science, Durham University, UK
Matthew Johnson
  • Department of Computer Science, Durham University, UK
Giacomo Paesani
  • Department of Computer Science, Durham University, UK
Daniël Paulusma
  • Department of Computer Science, Durham University, UK
Viktor Zamaraev
  • Department of Computer Science, Durham University, UK

Funding

  • Dabrowski, Konrad K.: Supported by EPSRC (EP/K025090/1) and the Leverhulme Trust (RPG-2016-258).
  • Johnson, Matthew: Supported by the Leverhulme Trust (RPG-2016-258).
  • Paulusma, Daniël: Supported by EPSRC (EP/K025090/1) and the Leverhulme Trust (RPG-2016-258).
  • Zamaraev, Viktor: Supported by EPSRC (EP/P020372/1).

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