Document Open Access Logo

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

PDF
Thumbnail PDF

File

LIPIcs.MFCS.2018.63.pdf
  • Filesize: 441 kB
  • 15 pages

Document Identifiers

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).

Cite AsGet BibTex

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

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).

Subject Classification

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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Rémy Belmonte, Pim van 't Hof, Marcin Kamiński, and Daniël Paulusma. The price of connectivity for feedback vertex set. Discrete Applied Mathematics, 217(Part 2):132-143, 2017. Google Scholar
  2. Marthe Bonamy, Konrad K. Dabrowski, Carl Feghali, Matthew Johnson, and Daniël Paulusma. Recognizing graphs close to bipartite graphs. Proc. MFCS 2017, LIPIcs, 83:70:1-70:14, 2017. Google Scholar
  3. Marthe Bonamy, Konrad K. Dabrowski, Carl Feghali, Matthew Johnson, and Daniël Paulusma. Independent feedback vertex set for P₅-free graphs. Algorithmica, to appear. Google Scholar
  4. Eglantine Camby. Price of independence for the dominating set problem. Manuscript, 2017. Google Scholar
  5. Eglantine Camby, Jean Cardinal, Samuel Fiorini, and Oliver Schaudt. The price of connectivity for vertex cover. Discrete Mathematics &Theoretical Computer Science, 16:207-224, 2014. Google Scholar
  6. Eglantine Camby and Fränk Plein. A note on an induced subgraph characterization of domination perfect graphs. Discrete Applied Mathematics, 217(Part 3):711-717, 2017. Google Scholar
  7. Eglantine Camby and Oliver Schaudt. The price of connectivity for dominating set: Upper bounds and complexity. Discrete Applied Mathematics, 177:53-59, 2014. Google Scholar
  8. Jean Cardinal and Eythan Levy. Connected vertex covers in dense graphs. Theoretical Computer Science, 411(26-28):2581-2590, 2010. Google Scholar
  9. Nina Chiarelli, Tatiana R. Hartinger, Matthew Johnson, Martin Milanič, and Daniël Paulusma. Minimum connected transversals in graphs: New hardness results and tractable cases using the price of connectivity. Theoretical Computer Science, 705:75-83, 2018. Google Scholar
  10. Thomas Emden-Weinert, Stefan Hougardy, and Bernd Kreuter. Uniquely colourable graphs and the hardness of colouring graphs of large girth. Combinatorics, Probability and Computing, 7(04):375-386, 1998. Google Scholar
  11. Alexander Grigoriev and René Sitters. Connected feedback vertex set in planar graphs. Proc. WG 2009, LNCS, 5911:143-153, 2010. Google Scholar
  12. Tatiana R. Hartinger, Matthew Johnson, Martin Milanič, and Daniël Paulusma. The price of connectivity for cycle transversals. European Journal of Combinatorics, 58:203-224, 2016. Google Scholar
  13. Matthew Johnson, Giacomo Paesani, and Daniël Paulusma. Connected vertex cover for (sP₁+P₅)-free graphs. Proc. WG 2018, LNCS, to appear. Google Scholar
  14. Daniel Král', Jan Kratochvíl, Zsolt Tuza, and Gerhard J. Woeginger. Complexity of coloring graphs without forbidden induced subgraphs. Proc. WG 2001, LNCS, 2204:254-262, 2001. Google Scholar
  15. Vadim V. Lozin and Marcin Kamiński. Coloring edges and vertices of graphs without short or long cycles. Contributions to Discrete Mathematics, 2(1), 2007. Google Scholar
  16. Neeldhara Misra, Geevarghese Philip, Venkatesh Raman, and Saket Saurabh. On parameterized independent feedback vertex set. Theoretical Computer Science, 461:65-75, 2012. Google Scholar
  17. Andrea Munaro. On line graphs of subcubic triangle-free graphs. Discrete Mathematics, 340(6):1210-1226, 2017. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact