Borradaile–Le–Sherman-Bennett conjecture on induced outerplanar subgraphs

Let $G$ be a planar graph of order $n$. The outerplanar subgraph number $s_o(G)$ is the maximum order of an induced outerplanar subgraph of $G$.

Borradaile–Le–Sherman-Bennett conjecture.

$$s_o(G)\ge\frac{2n}{3}.$$

The bound is known for 2-outerplanar graphs, but the general planar case remains open.