Skip to main content

Graph Editing to a Fixed Target

  • Conference paper
  • 838 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8288))

Abstract

For a fixed graph H, the H-Minor Edit problem takes as input a graph G and an integer k and asks whether G can be modified into H by a total of at most k edge contractions, edge deletions and vertex deletions. Replacing edge contractions by vertex dissolutions yields the H-Topological Minor Edit problem. For each problem we show polynomial-time solvable and NP-complete cases depending on the choice of H. Moreover, when G is AT-free, chordal or planar, we show that H-Minor Edit is polynomial-time solvable for all graphs H.

Research supported by EPSRC (EP/G043434/1) and ERC (267959).

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alon, N., Shapira, A., Sudakov, B.: Additive approximation for edge-deletion problems. In: Proc. FOCS 2005, pp. 419–428. IEEE Computer Society (2005)

    Google Scholar 

  2. Belmonte, R., Golovach, P.A., Heggernes, P., van, P.: Detecting fixed patterns in chordal graphs in polynomial time. Algorithmica (to appear)

    Google Scholar 

  3. Belmonte, R., van ’t Hof, P., Kamiński, M.: Induced Immersions. In: Chao, K.-M., Hsu, T.-S., Lee, D.-T. (eds.) ISAAC 2012. LNCS, vol. 7676, pp. 299–308. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  4. Burzyn, P., Bonomo, F., Duran, G.: NP-completeness results for edge modification problems. Discrete Applied Mathematics 154, 1824–1844 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Diestel, R.: Graph Theory, Electronic Edition. Springer (2005)

    Google Scholar 

  6. Downey, R.G., Fellows, M.R.: Parameterized complexity. Monographs in Computer Science. Springer, New York (1999)

    Book  Google Scholar 

  7. Fellows, M.R., Kratochvíl, J., Middendorf, M., Pfeiffer, F.: The complexity of induced minors and related problems. Algorithmica 13, 266–282 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fiala, J., Kamiński, M., Paulusma, D.: Detecting induced star-like minors in polynomial time. Journal of Discrete Algorithms 17, 74–85 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Golovach, P.A., van ’t Hof, P., Paulusma, D.: Obtaining planarity by contracting few edges. Theoretical Computer Science 476, 38–46 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Golovach, P.A., Kamiński, M., Paulusma, D., Thilikos, D.M.: Increasing the minimum degree of a graph by contractions. Theoretical Computer Science (to appear)

    Google Scholar 

  11. Golovach, P.A., Kratsch, D., Paulusma, D.: Detecting induced minors in AT-free graphs. Theoretical Computer Science (to appear)

    Google Scholar 

  12. Golovach, P.A., Paulusma, D., van Leeuwen, E.J.: Induced disjoint paths in AT-free graphs. In: Fomin, F.V., Kaski, P. (eds.) SWAT 2012. LNCS, vol. 7357, pp. 153–164. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  13. Grohe, M., Kawarabayashi, K., Marx, D., Wollan, P.: Finding topological subgraphs is fixed-parameter tractable. In: Proc. STOC 2011, pp. 479–488 (2011)

    Google Scholar 

  14. Haas, R., Hoffmann, M.: Chordless paths through three vertices. Theoretical Computer Science 351, 360–371 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Heggernes, P., van ’t Hof, P., Lévêque, B., Paul, C.: Contracting chordal graphs and bipartite graphs to paths and trees. Discrete Applied Mathematics (to appear)

    Google Scholar 

  16. Heggernes, P., van ’t Hof, P., Lokshtanov, D., Paul, C.: Obtaining a bipartite graph by contracting few edges. In: Proc. FSTTCS 2011, pp. 217–228 (2011)

    Google Scholar 

  17. Heggernes, P., van ’t Hof, P., Lévêque, B., Lokshtanov, D., Paul, C.: Contracting graphs to paths and trees. Algorithmica (to appear)

    Google Scholar 

  18. van ’t Hof, P., Kamiński, M., Paulusma, D., Szeider, S., Thilikos, D.M.: On graph contractions and induced minors. Discrete Applied Mathematics 160, 799–809 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kobayashi, Y., Kawarabayashi, K.: A linear time algorithm for the induced disjoint paths problem in planar graphs. Journal of Computer and System Sciences 78, 670–680 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lévêque, B., Lin, D.Y., Maffray, F., Trotignon, N.: Detecting induced subgraphs. Discrete Applied Mathematics 157, 3540–3551 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Lévêque, B., Maffray, F., Trotignon, N.: On graphs with no induced subdivision of K 4. Journal of Combinatorial Theory, Series B 102, 924–947 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lewis, J.M., Yannakakis, M.: The node-deletion problem for hereditary properties is NP-complete. Journal of Computer and System Sciences 20, 219–230 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  23. Natanzon, A., Shamir, R., Sharan, R.: Complexity classification of some edge modification problems. Discrete Applied Mathematics 113, 109–128 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  24. Papadimitriou, C.H., Yannakakis, M.: On limited nondeterminism and the complexity of the VC-dimension. Journal of Computer and System Sciences 43, 425–440 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  25. Robertson, N., Seymour, P.D.: Graph minors. XIII. The disjoint paths problem. Journal of Combinatorial Theory, Series B 63, 65–110 (1995)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Golovach, P.A., Paulusma, D., Stewart, I. (2013). Graph Editing to a Fixed Target. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45278-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45277-2

  • Online ISBN: 978-3-642-45278-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics