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Durham University

Research & business

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Publication details

Dabrowski, K.K., Golovach, P.A., van 't Hof, P., Paulusma, D. & Thilikos, D.M. (2017). Editing to a Planar Graph of Given Degrees. Journal of Computer and System Sciences 85: 168-182.

Author(s) from Durham

Abstract

We consider the following graph modification problem. Let the input consist of a graph G=(V,E), a weight function w:V∪E→N, a cost function c:V∪E→N0 and a degree function δ:V→N0, together with three integers kv,ke and C . The question is whether we can delete a set of vertices of total weight at most kv and a set of edges of total weight at most ke so that the total cost of the deleted elements is at most C and every non-deleted vertex v has degree δ(v) in the resulting graph G′. We also consider the variant in which G′ must be connected. Both problems are known to be NP-complete and W[1]-hard when parameterized by kv+ke. We prove that, when restricted to planar graphs, they stay NP-complete but have polynomial kernels when parameterized by kv+ke.