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.ICALP.2020.95
URN: urn:nbn:de:0030-drops-125027
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12502/
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Sau, Ignasi ; Stamoulis, Giannos ; Thilikos, Dimitrios M.

An FPT-Algorithm for Recognizing k-Apices of Minor-Closed Graph Classes

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Abstract

Let G be a graph class. We say that a graph G is a k-apex of G if G contains a set S of at most k vertices such that G⧵S belongs to G. We prove that if G is minor-closed, then there is an algorithm that either returns a set S certifying that G is a k-apex of G or reports that such a set does not exist, in 2^{poly(k)}n³ time. Here poly is a polynomial function whose degree depends on the maximum size of a minor-obstruction of G, i.e., the minor-minimal set of graphs not belonging to G. In the special case where G excludes some apex graph as a minor, we give an alternative algorithm running in 2^{poly(k)}n² time.

BibTeX - Entry

@InProceedings{sau_et_al:LIPIcs:2020:12502,
  author =	{Ignasi Sau and Giannos Stamoulis and Dimitrios M. Thilikos},
  title =	{{An FPT-Algorithm for Recognizing k-Apices of Minor-Closed Graph Classes}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{95:1--95:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12502},
  URN =		{urn:nbn:de:0030-drops-125027},
  doi =		{10.4230/LIPIcs.ICALP.2020.95},
  annote =	{Keywords: Graph modification problems, irrelevant vertex technique, graph minors, parameterized algorithms}
}

Keywords: Graph modification problems, irrelevant vertex technique, graph minors, parameterized algorithms
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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