Hof van 't, P. and Kaminski, M. and Paulusma, Daniel and Szeider, S. and Thilikos, D.M. (2010) 'On contracting graphs to fixed pattern graphs.', in *Theory and Practice of Computer Science, 36th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2010, Špindleruv Mlýn, Czech Republic, 23-29 January 2010 ; proceedings.* Berlin ; Heidelburg: Springer, pp. 503-514. Lecture notes in computer science. (5901).

## Abstract

For a fixed graph H, the H-Contractibility problem asks if a graph is H-contractible, i.e., can be transformed into H via a series of edge contractions. The computational complexity classification of this problem is still open. So far, H has a dominating vertex in all cases known to be polynomially solvable, 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 is polynomially solvable. Furthermore, 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. 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.

Item Type: | Book chapter |
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Full text: | Full text not available from this repository. |

Publisher Web site: | http://dx.doi.org/10.1007/978-3-642-11266-9_42 |

Record Created: | 07 Oct 2010 12:05 |

Last Modified: | 03 Apr 2013 13:22 |

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