Induced maximal outerplane subgraph conjecture

Let $G$ be a plane graph of sufficiently large order $n$. The outerplane subgraph number $s_{o'}(G)$ is the maximum order of an induced outerplane subgraph of $G$.

Induced maximal outerplane subgraph conjecture.

$$s_{o'}(G)\ge\frac{5n}{8}.$$

The construction in the paper gives examples with an induced maximal outerplane subgraph of order at most $5|V(G)|/8+1$; the supplied text does not state a resolution of this conjecture.