Minimum Order of a Cubic CND Graph

Determine the minimum order of a cubic, connected, nontraceable, detour graph.

Background

The thesis presents four cubic CND graphs of order 36 and proves that every cubic CND graph has order greater than 20. It does not determine the exact minimum order, motivating this problem.

References

What is the minimum order of a cubic, CND graph?

— Detours In Graphs  (2507.12086 - Bullock, 16 Jul 2025) in Chapter 2, Section "Open problems", Problem 3