par Van't Hof, Pim;Kaminski, Marcin 
;Paulusma, Daniël;Szeider, Stefan;Thilikos Touloupas, Dimitrios
Référence Lecture notes in computer science, 5901 LNCS, page (503-514)
Publication Publié, 2010
;Paulusma, Daniël;Szeider, Stefan;Thilikos Touloupas, Dimitrios Référence Lecture notes in computer science, 5901 LNCS, page (503-514)
Publication Publié, 2010
Article révisé par les pairs
| Résumé : | 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. © 2010 Springer-Verlag Berlin Heidelberg. |
