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Editing to a planar graph of given degrees.

Dabrowski, Konrad K. and Golovach, Petr A. and van 't Hof, Pim and Paulusma, Daniël and Thilikos, Dimitrios M. (2016) 'Editing to a planar graph of given degrees.', Journal of computer and system sciences., 85 . pp. 168-182.


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.

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Date accepted:26 November 2016
Date deposited:02 December 2016
Date of first online publication:01 December 2016
Date first made open access:No date available

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