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Graph Editing to a Fixed Target

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Combinatorial Algorithms (IWOCA 2013)

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

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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).

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References

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

    Google ScholarĀ 

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

    Google ScholarĀ 

  3. Belmonte, R., van ā€™t Hof, P., Kamiński, M.: Induced Immersions. In: Chao, K.-M., Hsu, T.-S., Lee, D.-T. (eds.) ISAAC 2012. LNCS, vol.Ā 7676, pp. 299ā€“308. Springer, Heidelberg (2012)

    ChapterĀ  Google ScholarĀ 

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

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

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

    Google ScholarĀ 

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

    BookĀ  Google ScholarĀ 

  7. Fellows, M.R., KratochvĆ­l, J., Middendorf, M., Pfeiffer, F.: The complexity of induced minors and related problems. AlgorithmicaĀ 13, 266ā€“282 (1995)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

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

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  9. Golovach, P.A., van ā€™t Hof, P., Paulusma, D.: Obtaining planarity by contracting few edges. Theoretical Computer ScienceĀ 476, 38ā€“46 (2013)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  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 ScholarĀ 

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

    Google ScholarĀ 

  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.Ā 7357, pp. 153ā€“164. Springer, Heidelberg (2012)

    ChapterĀ  Google ScholarĀ 

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

    Google ScholarĀ 

  14. Haas, R., Hoffmann, M.: Chordless paths through three vertices. Theoretical Computer ScienceĀ 351, 360ā€“371 (2006)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  15. Heggernes, P., van ā€™t Hof, P., LĆ©vĆŖque, B., Paul, C.: Contracting chordal graphs and bipartite graphs to paths and trees. Discrete Applied Mathematics (to appear)

    Google ScholarĀ 

  16. Heggernes, P., van ā€™t Hof, P., Lokshtanov, D., Paul, C.: Obtaining a bipartite graph by contracting few edges. In: Proc. FSTTCS 2011, pp. 217ā€“228 (2011)

    Google ScholarĀ 

  17. Heggernes, P., van ā€™t Hof, P., LĆ©vĆŖque, B., Lokshtanov, D., Paul, C.: Contracting graphs to paths and trees. Algorithmica (to appear)

    Google ScholarĀ 

  18. van ā€™t Hof, P., Kamiński, M., Paulusma, D., Szeider, S., Thilikos, D.M.: On graph contractions and induced minors. Discrete Applied MathematicsĀ 160, 799ā€“809 (2012)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

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

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  20. LĆ©vĆŖque, B., Lin, D.Y., Maffray, F., Trotignon, N.: Detecting induced subgraphs. Discrete Applied MathematicsĀ 157, 3540ā€“3551 (2009)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  21. LĆ©vĆŖque, B., Maffray, F., Trotignon, N.: On graphs with no induced subdivision of K 4. Journal of Combinatorial Theory, Series BĀ 102, 924ā€“947 (2012)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

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

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

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

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

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

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

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

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

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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

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  • 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

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