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arXiv · 2302.08938

Twin-width of Planar Graphs; a Short Proof

Petr Hliněný
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Abstract

The fascinating question of the maximum value of twin-width on planar graphs is nowadays not far from the 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. In the paper we give a short and simple self-contained proof that the twin-width of planar graphs is at most 11. We believe that this short proof can also shed more light on the topic of upper bound(s) on the twin-width of planar and beyond-planar graphs in general.

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Petr Hliněný. 2023-02-17. Twin-width of Planar Graphs; a Short Proof. https://arxiv.org/abs/2302.08938

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