License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2019.28
URN: urn:nbn:de:0030-drops-102677
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10267/
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Fomin, Fedor V. ; Golovach, Petr A. ; Thilikos, Dimitrios M.

Modification to Planarity is Fixed Parameter Tractable

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LIPIcs-STACS-2019-28.pdf (0.8 MB)

Abstract

A replacement action is a function L that maps each k-vertex labeled graph to another k-vertex graph. We consider a general family of graph modification problems, called L-Replacement to C, where the input is a graph G and the question is whether it is possible to replace in G some k-vertex subgraph H of it by L(H) so that the new graph belongs to the graph class C. L-Replacement to C can simulate several modification operations such as edge addition, edge removal, edge editing, and diverse completion and superposition operations. In this paper, we prove that for any action L, if C is the class of planar graphs, there is an algorithm that solves L-Replacement to C in O(|G|^{2}) steps. We also present several applications of our approach to related problems.

BibTeX - Entry

@InProceedings{fomin_et_al:LIPIcs:2019:10267,
  author =	{Fedor V. Fomin and Petr A. Golovach and Dimitrios M. Thilikos},
  title =	{{Modification to Planarity is Fixed Parameter Tractable}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{28:1--28:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Rolf Niedermeier and Christophe Paul},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10267},
  doi =		{10.4230/LIPIcs.STACS.2019.28},
  annote =	{Keywords: Modification problems, Planar graphs, Irrelevant vertex technique}
}

Keywords: Modification problems, Planar graphs, Irrelevant vertex technique
Collection: 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)
Issue Date: 2019
Date of publication: 12.03.2019

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