Editing to a Connected Graph of Given Degrees

  • Petr A. Golovach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8635)


The aim of edge editing or modification problems is to change a given graph by adding and deleting of a small number of edges in order to satisfy a certain property. We consider the Edge Editing to a Connected Graph of Given Degrees problem that for a given graph G, non-negative integers d,k and a function δ : V(G) → {1,…,d}, asks whether it is possible to obtain a connected graph G′ from G such that the degree of v is δ(v) for any vertex v by at most k edge editing operations. As the problem is NP-complete even if δ(v) = 2, we are interested in the parameterized complexity and show that Edge Editing to a Connected Graph of Given Degrees admits a polynomial kernel when parameterized by d + k. For the special case δ(v) = d, i.e., when the aim is to obtain a connected d-regular graph, the problem is shown to be fixed parameter tractable when parameterized by k only.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alon, N., Shapira, A., Sudakov, B.: Additive approximation for edge-deletion problems. In: FOCS, pp. 419–428. IEEE Computer Society (2005)Google Scholar
  2. 2.
    Burzyn, P., Bonomo, F., Durán, G.: NP-completeness results for edge modification problems. Discrete Applied Mathematics 154(13), 1824–1844 (2006)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Inf. Process. Lett. 58(4), 171–176 (1996)CrossRefMATHGoogle Scholar
  4. 4.
    Flum, J., Grohe, M.: Parameterized complexity theory. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin (2006)Google Scholar
  5. 5.
    Golovach, P.A.: Editing to a connected graph of given degrees. CoRR abs/1308.1802 (2013)Google Scholar
  6. 6.
    Khot, S., Raman, V.: Parameterized complexity of finding subgraphs with hereditary properties. Theor. Comput. Sci. 289(2), 997–1008 (2002)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Lewis, J.M., Yannakakis, M.: The node-deletion problem for hereditary properties is np-complete. J. Comput. Syst. Sci. 20(2), 219–230 (1980)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Mathieson, L., Szeider, S.: Editing graphs to satisfy degree constraints: A parameterized approach. J. Comput. Syst. Sci. 78(1), 179–191 (2012)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Moser, H., Thilikos, D.M.: Parameterized complexity of finding regular induced subgraphs. J. Discrete Algorithms 7(2), 181–190 (2009)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Natanzon, A., Shamir, R., Sharan, R.: Complexity classification of some edge modification problems. Discrete Applied Mathematics 113(1), 109–128 (2001)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Niedermeier, R.: Invitation to fixed-parameter algorithms. Oxford Lecture Series in Mathematics and its Applications, vol. 31. Oxford University Press, Oxford (2006)CrossRefMATHGoogle Scholar
  12. 12.
    Ryser, H.J.: Combinatorial mathematics. The Carus Mathematical Monographs, vol. 14. Published by The Mathematical Association of America (1963)Google Scholar
  13. 13.
    Yannakakis, M.: Node- and edge-deletion NP-complete problems. In: Lipton, R.J., Burkhard, W.A., Savitch, W.J., Friedman, E.P., Aho, A.V. (eds.) STOC, pp. 253–264. ACM (1978)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Petr A. Golovach
    • 1
    • 2
  1. 1.Department of InformaticsUniversity of BergenNorway
  2. 2.Steklov Institute of Mathematics at St.PetersburgRussian Academy of SciencesRussia

Personalised recommendations