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The structural parameter twin-width was introduced by Bonnet et al. in [FOCS2020], and already this first paper included an asymptotic argument boundingthe twin-width of planar graphs by a non-explicit constant. Quite recently, wehave 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 37by Bekos et al. [arXiv, April 2022]. We prove that the twin-width of planargraphs is at most 9. Furthermore, if a planar graph is also bipartite, then itstwin-width is at most 6.

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