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
Alon, N., Shapira, A., Sudakov, B.: Additive approximation for edge-deletion problems. In: Proc. FOCS 2005, pp. 419–428. IEEE Computer Society (2005)
Belmonte, R., Golovach, P.A., Heggernes, P., van, P.: Detecting fixed patterns in chordal graphs in polynomial time. Algorithmica (to appear)
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)
Burzyn, P., Bonomo, F., Duran, G.: NP-completeness results for edge modification problems. Discrete Applied Mathematics 154, 1824–1844 (2006)
Diestel, R.: Graph Theory, Electronic Edition. Springer (2005)
Downey, R.G., Fellows, M.R.: Parameterized complexity. Monographs in Computer Science. Springer, New York (1999)
Fellows, M.R., Kratochvíl, J., Middendorf, M., Pfeiffer, F.: The complexity of induced minors and related problems. Algorithmica 13, 266–282 (1995)
Fiala, J., Kamiński, M., Paulusma, D.: Detecting induced star-like minors in polynomial time. Journal of Discrete Algorithms 17, 74–85 (2012)
Golovach, P.A., van ’t Hof, P., Paulusma, D.: Obtaining planarity by contracting few edges. Theoretical Computer Science 476, 38–46 (2013)
Golovach, P.A., Kamiński, M., Paulusma, D., Thilikos, D.M.: Increasing the minimum degree of a graph by contractions. Theoretical Computer Science (to appear)
Golovach, P.A., Kratsch, D., Paulusma, D.: Detecting induced minors in AT-free graphs. Theoretical Computer Science (to appear)
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)
Grohe, M., Kawarabayashi, K., Marx, D., Wollan, P.: Finding topological subgraphs is fixed-parameter tractable. In: Proc. STOC 2011, pp. 479–488 (2011)
Haas, R., Hoffmann, M.: Chordless paths through three vertices. Theoretical Computer Science 351, 360–371 (2006)
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)
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)
Heggernes, P., van ’t Hof, P., Lévêque, B., Lokshtanov, D., Paul, C.: Contracting graphs to paths and trees. Algorithmica (to appear)
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)
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)
Lévêque, B., Lin, D.Y., Maffray, F., Trotignon, N.: Detecting induced subgraphs. Discrete Applied Mathematics 157, 3540–3551 (2009)
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)
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)
Natanzon, A., Shamir, R., Sharan, R.: Complexity classification of some edge modification problems. Discrete Applied Mathematics 113, 109–128 (2001)
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)
Robertson, N., Seymour, P.D.: Graph minors. XIII. The disjoint paths problem. Journal of Combinatorial Theory, Series B 63, 65–110 (1995)
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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
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