  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.
