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.
CITATION STYLE
Van’T Hof, P., Kamiński, M., Paulusma, D., Szeider, S., & Thilikos, D. M. (2010). On contracting graphs to fixed pattern graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5901 LNCS, pp. 503–514). https://doi.org/10.1007/978-3-642-11266-9_42
Mendeley helps you to discover research relevant for your work.