Screewidth of outerplanar graphs

Determine whether the screewidth of outerplanar graphs on n vertices is bounded by O(√n).

Background

The paper notes that the upper bounds obtained for the fan and wheel graphs can also be derived using screewidth, although screewidth is not used in the proof of the principal outerplanar result. This observation motivates the unresolved question of whether all outerplanar graphs have screewidth of square-root order.

References

As a consequence, we obtain the following open question: Is the screewidth of outerplanar graphs bounded by $O(\sqrt{n})$?

— The scramble number of outerplanar graphs  (2609.03755 - Laboy, 3 Sep 2026) in Section 5, Open Questions