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, also WG'22], 583 by Bonnet et al. [arXiv, February 2022], of 37 by Bekos et al. [arXiv, April 2022], and of 9 by the first author [arXiv, June 2022]. We further elaborate on the approach used in the last paper and improve the upper bound to 8. This is already very close to the currently best lower bound of 7 by Kr\'al and Lamaison [arXiv, September 2022]. We some of the new ideas, we also significantly simplify the previous proof of the first author [arXiv, August 2022] that the twin-width of bipartite planar graphs is at most 6.
翻译：Bonneet等人在[FOCS 2020]中提出了结构参数双边线,这第一份论文已经包括了用一个非明白的常数将平面图的双边线捆绑起来的无症状论据。最近,我们第一次看到Jacob和Pilipczuk[ArXiv, 2022年1月, 也是WG'22]、Bonnet等人[arXiv, 20222年2月]、Bekos等人[arXiv, 20222年4月]、Bekos等人[ARXiv, 2022年4年4月]37和第一作者[ARXiv, 2022年6月]的9张平面图的细小的明显上边线。我们进一步阐述了上方图中使用的方法,并将上方线改进为8号。这已经非常接近Kr\al和Lamaisson[arXiv, 2022年9月 2022日]目前最低的7号最低的界线。我们的一些新想法也大大简化了第一作者[arXiv,2022年8月2022号]以前的证据,即两边图的双边图的双边图的两边图的两边最接近于6号。
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