Unrestricted asymptotic coefficient for W_{3,4}-free planar graphs

Determine the unrestricted asymptotic coefficient of the planar Turán number for W_{3,4}, beyond the subclass of planar graphs containing a dominating vertex.

Background

The paper determines the exact extremal number for W_{3,4}-free planar graphs with a dominating vertex and obtains the coefficient 5/2 for that subclass. It explicitly states that the corresponding asymptotic coefficient for unrestricted W_{3,4}-free planar graphs remains unresolved.

References

Its unrestricted asymptotic coefficient, and the existence of $W_{3,4}$-free triangulations on ten or eleven vertices, are not settled by these arguments.

— Sharp planar Turán bounds for quasi-double stars  (2610.05706 - Shao et al., 5 Oct 2026) in Section 5, “Concluding questions”