Exact planar Turán numbers for W_{2,4} in remaining residue classes

Determine the exact planar Turán number ex(n,W_{2,4}) for orders n not divisible by eight, beyond the established upper bound and the equality cases at multiples of eight.

Background

The paper proves ex(n,W_{2,4}) ≤ floor(9n/4) for every n and attains equality when 8 divides n. The exact extremal function is therefore known at those orders, but the authors identify determining the values in the other residue classes as an unresolved finite-order problem.

References

Determining $ex_{}(n,W_{2,4})$ in the remaining residue classes is still a finite-order problem.

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