Borradaile, Le and Sherman-Bennett [Graphs and Combinatorics, 2017] proved that every $n$-vertex $2$-outerplane graph has a set of at least $2n/3$ vertices that induces an outerplane graph. We identify a major flaw in their proof and recover their result with a different, and unfortunately much more complex, proof.

翻译：Borradaile、Le和Sherman-Bennett [Graphs and Combinatorics, 2017] 证明了每个具有n个顶点的2-外平面图都存在一个至少包含2n/3个顶点的集合，该集合诱导出一个外平面子图。我们在其证明中发现了一个重大缺陷，并通过一种不同且更为复杂的证明方法重新验证了该结论。