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DOI: 10.4230/LIPIcs.SWAT.2016.4

A Linear Kernel for Finding Square Roots of Almost Planar Graphs

Authors: Petr A. Golovach, Dieter Kratsch, Daniël Paulusma, and Anthony Stewart

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

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 of distance 2 of 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 is a graph that can be made planar by the removal of at most k vertices. We prove that the generalization of Square Root, in which we are given two subsets of edges prescribed to be in or out of a square root, respectively, 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.

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Petr A. Golovach, Dieter Kratsch, Daniël Paulusma, and Anthony Stewart. A Linear Kernel for Finding Square Roots of Almost Planar Graphs. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{golovach_et_al:LIPIcs.SWAT.2016.4,
  author =	{Golovach, Petr A. and Kratsch, Dieter and Paulusma, Dani\"{e}l and Stewart, Anthony},
  title =	{{A Linear Kernel for Finding Square Roots of Almost Planar Graphs}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{4:1--4:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.4},
  URN =		{urn:nbn:de:0030-drops-60333},
  doi =		{10.4230/LIPIcs.SWAT.2016.4},
  annote =	{Keywords: planar graphs, square roots, linear kernel}
}

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A Linear Kernel for Finding Square Roots of Almost Planar Graphs

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