Abreu–Diwan–Jackson–Labbate–Schwenk's classification conjecture for 3-edge-connected 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 star product is the cubic graph operation that deletes one degree-3 vertex from each factor and joins the three resulting pairs of neighbours. Let $G$ be a 3-edge-connected cubic bipartite graph.

Abreu–Diwan–Jackson–Labbate–Schwenk's conjecture. $G$ is pseudo 2-factor isomorphic if and only if $G$ can be obtained from $K_{3,3}$, the Heawood graph or the Pappus graph by repeated star products.

This conjecture gives a proposed classification of all 3-edge-connected cubic bipartite graphs with the parity property. The supplied text gives no resolution of this statement.