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DOI: 10.4230/LIPIcs.ESA.2022.62
URN: urn:nbn:de:0030-drops-170007
URL: https://drops.dagstuhl.de/opus/volltexte/2022/17000/
Goetze, Miriam ; Jungeblut, Paul ; Ueckerdt, Torsten
Efficient Recognition of Subgraphs of Planar Cubic Bridgeless Graphs
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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 𝒪(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 | |
| Seminar: | 30th Annual European Symposium on Algorithms (ESA 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 01.09.2022 |
