Kaminski, M. and Paulusma, Daniel and Thilikos, D.M. (2010) 'Contractions of planar graphs in polynomial time.', in Algorithms : ESA 2010 : 18th Annual European Symposium, 6-8 September 2010, Liverpool UK ; proceedings part I. Berlin ; Heidelberg: Springer, pp. 122-133. Lecture notes in computer science. (6346).
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.
|Item Type:||Book chapter|
|Keywords:||Planar graph, Dual graph, Contraction, Topological minor.|
|Full text:||Full text not available from this repository.|
|Publisher Web site:||http://dx.doi.org/10.1007/978-3-642-15775-2_11|
|Date accepted:||No date available|
|Date deposited:||No date available|
|Date of first online publication:||2010|
|Date first made open access:||No date available|
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