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Publications in Scientific Journals:

P. Hof, M. Kaminski, D. Paulusma, St. Szeider, D. Thilikos:
"On Graph Contractions and Induced Minors";
Discrete Applied Mathematics, Vol. 160 (2012), No. 6; 799 - 809.



English 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.

Keywords:
Graph contraction; Graph induced minor; Graph minor


"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.dam.2010.05.005



Related Projects:
Project Head Stefan Szeider:
The Parameterized Complexity of Reasoning Problems


Created from the Publication Database of the Vienna University of Technology.