Abreu–Diwan–Jackson–Labbate–Schwenk's constituent classification conjecture for pseudo 2-factor isomorphic graphs

A graph is pseudo 2-factor isomorphic if all of its 2-factors have the same parity of number of cycles. A cubic graph is essentially 4-edge-connected if it has no non-trivial 3-edge-cuts. Let $G$ be an essentially 4-edge-connected pseudo 2-factor isomorphic cubic bipartite graph.

Abreu–Diwan–Jackson–Labbate–Schwenk's conjecture. $G$ must be $K_{3,3}$, the Heawood graph or the Pappus graph.

The conjecture is the essentially 4-edge-connected case of the broader classification conjecture. It was refuted by a computer-search counterexample constructed by Goedgebeur, and consequently the broader conjecture was refuted as well.