Construct a biplanar graph with independence ratio below 2/17

Construct a biplanar graph whose independence ratio is below 2/17, thereby resolving Open Problem 2 of Gethner and Sulanke.

Background

The paper identifies this as one of two smaller questions that remain open. A biplanar graph on 18 vertices with independence number 2 would have independence ratio 1/9, which is below 2/17. The main theorem rules out such graphs on orders other than 18, so the unresolved search is effectively concentrated on the 18-vertex case, subject to the adapted filtering conditions described by the authors.