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arXiv · 2205.05378

Twin-width of Planar Graphs is at most 9, and at most 6 when Bipartite Planar

Petr Hliněný
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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.

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Petr Hliněný. 2022-08-29. Twin-width of Planar Graphs is at most 9, and at most 6 when Bipartite Planar. https://arxiv.org/abs/2205.05378

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