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A Linear Kernel for Finding Square Roots of Almost Planar Graphs

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

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Petr A. Golovach
Dieter Kratsch
Daniël Paulusma
Anthony Stewart

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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) https://doi.org/10.4230/LIPIcs.SWAT.2016.4

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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Keywords
  • planar graphs
  • square roots
  • linear kernel

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