CND Graphs of Arbitrarily Large Girth

Determine whether connected, nontraceable, detour graphs exist with arbitrarily large girth.

Background

The constructions in the thesis produce CND graphs with girth at most 7, including families of girth 6 and 7. The authors do not know whether the girth of CND graphs is unbounded.

References

Do there exist CND graphs of arbitrarily large girth?

Detours In Graphs  (2507.12086 - Bullock, 16 Jul 2025) in Chapter 2, Section "Open problems", Problem 5