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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.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.jcss.2016.11.009
Publisher statement:This article is available under the terms of the Creative Commons Attribution License (CC BY). You may copy and distribute the article, create extracts, abstracts and new works from the article, alter and revise the article, text or data mine the article and otherwise reuse the article commercially (including reuse and/or resale of the article) without permission from Elsevier. You must give appropriate credit to the original work, together with a link to the formal publication through the relevant DOI and a link to the Creative Commons user license above. You must indicate if any changes are made but not in any way that suggests the licensor endorses you or your use of the work.
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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