Twin-width of Planar Graphs; a Short Proof

Abstract

The fascinating question of the maximum value of twin-width on planar graphs is nowadays not far from a final resolution; there is a lower bound of~$7$ coming from a construction by Kr\'al' and Lamaison [arXiv, September 2022], and an upper bound of~$8$ by Hlin\v{e}n\'y and Jedelsk\'y [arXiv, October 2022]. The upper bound (currently best) of~$8$, however, is rather complicated and involved. We give a short and simple self-contained proof that the twin-width of planar graphs is at most~$11$.