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A linear kernel for finding square roots of almost planar graphs.

Golovach, P.A. and Kratsch, D. and Paulusma, D. and Stewart, A. (2017) 'A linear kernel for finding square roots of almost planar graphs.', Theoretical computer science., 689 . pp. 36-47.

Abstract

A graph H is a square root of a graph G if G can be obtained from H by the addition of edges between any two vertices in H that are at distance 2 from each other. The Square Root problem is that of deciding whether a given graph admits a square root. We consider this problem for planar graphs in the context of the “distance from triviality” framework. For an integer k , a planar+kv graph (or k-apex graph) is a graph that can be made planar by the removal of at most k vertices. We prove that a generalization of Square Root, in which some edges are prescribed to be either in or out of any solution, has a kernel of size O(k) for planar+kv graphs, when parameterized by k. Our result is based on a new edge reduction rule which, as we shall also show, has a wider applicability for the Square Root problem.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.tcs.2017.05.008
Publisher statement:© 2017 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:11 May 2017
Date deposited:23 May 2017
Date of first online publication:25 May 2017
Date first made open access:25 May 2018

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