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@inproceedings{2294838,
author = {Hliněný, Petr and Jedelský, Jan},
address = {Dagstuhl, Germany},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
doi = {http://dx.doi.org/10.4230/LIPIcs.ICALP.2023.75},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
keywords = {twin-width; planar graph},
howpublished = {elektronická verze "online"},
language = {eng},
location = {Dagstuhl, Germany},
isbn = {978-3-95977-278-5},
pages = {"75:1"-"75:18"},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
title = {Twin-width of Planar Graphs is at most 8, and at most 6 when Bipartite Planar},
year = {2023}
}
TY - JOUR
ID - 2294838
AU - Hliněný, Petr - Jedelský, Jan
PY - 2023
TI - Twin-width of Planar Graphs is at most 8, and at most 6 when Bipartite Planar
PB - Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik
CY - Dagstuhl, Germany
SN - 9783959772785
KW - twin-width
KW - planar graph
N2 - Twin-width is a structural width parameter introduced by Bonnet, Kim, Thomassé and Watrigant [FOCS 2020]. Very briefly, its essence is a gradual reduction (a contraction sequence) of the given graph down to a single vertex while maintaining limited difference of neighbourhoods of the vertices, and it can be seen as widely generalizing several other traditional structural parameters. Having such a sequence at hand allows us to solve many otherwise hard problems efficiently. Graph classes of bounded twin-width, in which appropriate contraction sequences are efficiently constructible, are thus of interest in combinatorics and in computer science. However, we currently do not know in general how to obtain a witnessing contraction sequence of low width efficiently, and published upper bounds on the twin-width in non-trivial cases are often "astronomically large". We focus on planar graphs, which are known to have bounded twin-width (already since the introduction of twin-width), but the first explicit "non-astronomical" upper bounds on the twin-width of planar graphs appeared just a year ago; namely the bound of at most 183 by Jacob and Pilipczuk [arXiv, January 2022], and 583 by Bonnet, Kwon and Wood [arXiv, February 2022]. Subsequent arXiv manuscripts in 2022 improved the bound down to 37 (Bekos et al.), 11 and 9 (both by Hliněný). We further elaborate on the approach used in the latter manuscripts, proving that the twin-width of every planar graph is at most 8, and construct a witnessing contraction sequence in linear time. Note that the currently best lower-bound planar example is of twin-width 7, by Král' and Lamaison [arXiv, September 2022]. We also prove that the twin-width of every bipartite planar graph is at most 6, and again construct a witnessing contraction sequence in linear time.
ER -
HLINĚNÝ, Petr and Jan JEDELSKÝ. Twin-width of Planar Graphs is at most 8, and at most 6 when Bipartite Planar. Online. In Etessami, Kousha and Feige, Uriel and Puppis, Gabriele. \textit{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}. Dagstuhl, Germany: Schloss Dagstuhl -- Leibniz-Zentrum f$\{\backslash$''u$\}$r Informatik, 2023, p.~''75:1''-''75:18'', 18 pp. ISBN~978-3-95977-278-5. Available from: https://dx.doi.org/10.4230/LIPIcs.ICALP.2023.75.
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