par Belmonte, Rémy;Golovach, Petr A.;Heggernes, Pinar;van 't Hof, Pim;Kaminski, Marcin 
;Paulusma, Daniël
Référence Lecture notes in computer science, 7074 LNCS, page (110-119)
Publication Publié, 2011
;Paulusma, DaniëlRéférence Lecture notes in computer science, 7074 LNCS, page (110-119)
Publication Publié, 2011
Article révisé par les pairs
| Résumé : | The k-Disjoint Paths problem, which takes as input a graph G and k pairs of specified vertices (s i ,t i ), asks whether G contains k mutually vertex-disjoint paths P i such that P i connects s i and t i, for i=1,...,k. We study a natural variant of this problem, where the vertices of P i must belong to a specified vertex subset U i for i=1,...,k. In contrast to the original problem, which is polynomial-time solvable for any fixed integer k, we show that this variant is NP-complete even for k = 2. On the positive side, we prove that the problem becomes polynomial-time solvable for any fixed integer k if the input graph is chordal. We use this result to show that, for any fixed graph H, the problems H-Contractibility and H-Induced Minor can be solved in polynomial time on chordal graphs. These problems are to decide whether an input graph G contains H as a contraction or as an induced minor, respectively. © 2011 Springer-Verlag. |
