Girth of D(k,3)

Determine the girth of D(k,3) for every integer k≥2.

Background

The paper notes that the general girth conjecture for D(k,q) has different and incompletely understood behavior when q=3. Known values and upper bounds are available only for selected k.

References

Problem 8. Determine the girth of D(k, 3) for all k ≥ 2.

— Some families of graphs, hypergraphs and digraphs defined by systems of equations  (2503.07915 - Lazebnik et al., 10 Mar 2025) in Problem 8, Section 6.3