Twin-width of Planar Graphs is at most 9, and at most 6 when Bipartite Planar
Combinatorics
2022-08-31 v4
Abstract
The structural parameter twin-width was introduced by Bonnet et al. in [FOCS 2020], and already this first paper included an asymptotic argument bounding the twin-width of planar graphs by a non-explicit constant. Quite recently, we have seen first small explicit upper bounds of 183 by Jacob and Pilipczuk [arXiv, January 2022], 583 by Bonnet et al. [arXiv, February 2022], and of 37 by Bekos et al. [arXiv, April 2022]. We prove that the twin-width of planar graphs is at most 9. Furthermore, if a planar graph is also bipartite, then its twin-width is at most 6.
Cite
@article{arxiv.2205.05378,
title = {Twin-width of Planar Graphs is at most 9, and at most 6 when Bipartite Planar},
author = {Petr Hliněný},
journal= {arXiv preprint arXiv:2205.05378},
year = {2022}
}