P.A. Golovach
A linear kernel for finding square roots of almost planar graphs
Golovach, P.A.; Kratsch, D.; Paulusma, D.; Stewart, A.
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.
Citation
Golovach, P., Kratsch, D., Paulusma, D., & Stewart, A. (2017). A linear kernel for finding square roots of almost planar graphs. Theoretical Computer Science, 689, 36-47. https://doi.org/10.1016/j.tcs.2017.05.008
Journal Article Type | Article |
---|---|
Acceptance Date | May 11, 2017 |
Online Publication Date | May 25, 2017 |
Publication Date | May 25, 2017 |
Deposit Date | May 20, 2017 |
Publicly Available Date | May 25, 2018 |
Journal | Theoretical Computer Science |
Print ISSN | 0304-3975 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 689 |
Pages | 36-47 |
DOI | https://doi.org/10.1016/j.tcs.2017.05.008 |
Public URL | https://durham-repository.worktribe.com/output/1378642 |
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Copyright 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/
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