Contractions of planar graphs in polynomial time

Kaminski, M.; Paulusma, D.; Thilikos, D.M.

Abstract

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.

Citation

Kaminski, M., Paulusma, D., & Thilikos, D. (2010, December). Contractions of planar graphs in polynomial time. Presented at The 18th Annual European Symposium

• Presentation Conference Type: Conference Paper (published)
• Conference Name: The 18th Annual European Symposium
• Publication Date: Jan 1, 2010
• Deposit Date: Oct 6, 2010
• Print ISSN: 0302-9743
• Pages: 122-133
• Series Title: Lecture notes in computer science
• Series Number: 6346
• Series ISSN: 0302-9743,1611-3349
• Edition: 18th
• Book Title: Algorithms : ESA 2010 : 18th Annual European Symposium, 6-8 September 2010, Liverpool UK ; proceedings part I.
• DOI: https://doi.org/10.1007/978-3-642-15775-2_11
• Keywords: Planar graph, Dual graph, Contraction, Topological minor.
• Public URL: https://durham-repository.worktribe.com/output/1159699