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.ESA.2020.48
URN: urn:nbn:de:0030-drops-129144
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12914/
Fomin, Fedor V. ;
Golovach, Petr A.
Kernelization of Whitney Switches
Abstract
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
@InProceedings{fomin_et_al:LIPIcs:2020:12914,
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 = {https://drops.dagstuhl.de/opus/volltexte/2020/12914},
URN = {urn:nbn:de:0030-drops-129144},
doi = {10.4230/LIPIcs.ESA.2020.48},
annote = {Keywords: Whitney switch, 2-isomorphism, Parameterized Complexity, kernelization}
}
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Keywords: |
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Whitney switch, 2-isomorphism, Parameterized Complexity, kernelization |
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Collection: |
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28th Annual European Symposium on Algorithms (ESA 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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26.08.2020 |
