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On graph contractions and induced minors. \ud

By P. van 't Hof, M. Kaminski, Daniel Paulusma, S. Szeider and D.M. Thilikos

Abstract

The Induced Minor Containment problem takes as input two graphs G and H, and asks whether G has H as an induced minor. We show that this problem is fixed parameter tractable in |VH| if G belongs to any nontrivial minor-closed graph class and H is a planar graph. For a fixed graph H, the H-Contractibility problem is to decide whether a graph can be contracted to H. The computational complexity classification of this problem is still open. So far, H has a dominating vertex in all cases known to be solvable in polynomial time, whereas H does not have such a vertex in all cases known to be NP-complete. Here, we present a class of graphs H with a dominating vertex for which H-Contractibility is NP-complete. We also present a new class of graphs H for which H-Contractibility can be solved in polynomial time. Finally, we study the (H,v)-Contractibility problem, where v is a vertex of H. The input of this problem is a graph G and an integer k, and the question is whether G is H-contractible such that the “bag” of G corresponding to v contains at least k vertices. We show that this problem is NP-complete whenever H is connected and v is not a dominating vertex of H.\ud \u

Topics: Graph contraction, Graph induced minor, Graph minor.
Publisher: Elsevier
Year: 2012
DOI identifier: 10.1016/j.dam.2010.05.005
OAI identifier: oai:dro.dur.ac.uk.OAI2:7421
Journal:

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Citations

  1. A fast and high quality multilevel scheme for partitioning irregular graphs. doi
  2. (1995). Graph minors. XIII. The disjoint paths problem. doi
  3. (2008). The computational complexity of graph contractions I: polynomially solvable and NP-complete cases. doi
  4. The computational complexity of graph contractions II: two tough polynomially solvable cases. doi
  5. (2004). Wagner's conjecture. doi

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