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Contractions of planar graphs in polynomial time

par Kaminski, Marcin ;Paulusma, Daniël;Thilikos Touloupas, Dimitrios
Référence Lecture notes in computer science, 6346 LNCS, PART 1, page (122-133)
Publication Publié, 2010

Article révisé par les pairs

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Résumé :

We prove that for every graph H, there exists a polynomial-time algorithm deciding if a planar graph can be contracted to H. We introduce contractions and topological minors of embedded (plane) graphs and show that a plane graph H is an embedded contraction of a plane graph G, if and only if, the dual of H is an embedded topological minor of the dual of G. We show how to reduce finding embedded topological minors in plane graphs to solving an instance of the disjoint paths problem. Finally, we extend the result to graphs embeddable in an arbitrary surface. © 2010 Springer-Verlag.