Cycle lengths in linearized Wenger graphs

Determine the lengths of all cycles in the linearized Wenger graph Lm(q).

Background

The paper records several known cycle-length results for linearized Wenger graphs, including their girth and the existence of cycles of specified even lengths. A complete characterization of the cycle lengths remains unresolved.

References

Problem 2. Determine the lengths of all cycles in the linearized Wenger graph Lm(q).

— Some families of graphs, hypergraphs and digraphs defined by systems of equations  (2503.07915 - Lazebnik et al., 10 Mar 2025) in Problem 2, Section 4.5.2