License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2022.62
URN: urn:nbn:de:0030-drops-170007
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17000/
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Goetze, Miriam ; Jungeblut, Paul ; Ueckerdt, Torsten

Efficient Recognition of Subgraphs of Planar Cubic Bridgeless Graphs

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LIPIcs-ESA-2022-62.pdf (0.8 MB)

Abstract

It follows from the work of Tait and the Four-Color-Theorem that a planar cubic graph is 3-edge-colorable if and only if it contains no bridge. We consider the question of which planar graphs are subgraphs of planar cubic bridgeless graphs, and hence 3-edge-colorable. We provide an efficient recognition algorithm that given an n-vertex planar graph, augments this graph in ?(n²) steps to a planar cubic bridgeless supergraph, or decides that no such augmentation is possible. The main tools involve the Generalized (Anti)factor-problem for the fixed embedding case, and SPQR-trees for the variable embedding case.

BibTeX - Entry

@InProceedings{goetze_et_al:LIPIcs.ESA.2022.62,
  author =	{Goetze, Miriam and Jungeblut, Paul and Ueckerdt, Torsten},
  title =	{{Efficient Recognition of Subgraphs of Planar Cubic Bridgeless Graphs}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{62:1--62:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17000},
  URN =		{urn:nbn:de:0030-drops-170007},
  doi =		{10.4230/LIPIcs.ESA.2022.62},
  annote =	{Keywords: edge colorings, planar graphs, cubic graphs, generalized factors, SPQR-tree}
}

Keywords: edge colorings, planar graphs, cubic graphs, generalized factors, SPQR-tree
Collection: 30th Annual European Symposium on Algorithms (ESA 2022)
Issue Date: 2022
Date of publication: 01.09.2022

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