License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ESA.2020.48
URN: urn:nbn:de:0030-drops-129144
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Fomin, Fedor V. ; Golovach, Petr A.

Kernelization of Whitney Switches

LIPIcs-ESA-2020-48.pdf (0.7 MB)


A fundamental theorem of Whitney from 1933 asserts that 2-connected graphs G and H are 2-isomorphic, or equivalently, their cycle matroids are isomorphic, if and only if G can be transformed into H by a series of operations called Whitney switches. In this paper we consider the quantitative question arising from Whitney’s theorem: Given 2-isomorphic graphs, can we transform one into another by applying at most k Whitney switches? This problem is already NP-complete for cycles, and we investigate its parameterized complexity. We show that the problem admits a kernel of size ?(k), and thus, is fixed-parameter tractable when parameterized by k.

BibTeX - Entry

  author =	{Fedor V. Fomin and Petr A. Golovach},
  title =	{{Kernelization of Whitney Switches}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{48:1--48:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-129144},
  doi =		{10.4230/LIPIcs.ESA.2020.48},
  annote =	{Keywords: Whitney switch, 2-isomorphism, Parameterized Complexity, kernelization}

Keywords: Whitney switch, 2-isomorphism, Parameterized Complexity, kernelization
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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