Fleischner–Jackson–Litsyn–Swart's classification conjecture for 2-factor Hamiltonian regular bipartite graphs

A 2-factor of a graph is a 2-regular spanning subgraph, and a graph is 2-factor Hamiltonian if every 2-factor is a Hamiltonian cycle. A star product of cubic graphs is the operation that deletes one degree-3 vertex from each graph and joins the resulting three pairs of neighbours. Let $G$ be a 2-factor Hamiltonian $k$-regular bipartite graph.

Fleischner–Jackson–Litsyn–Swart's conjecture. Either $k=2$ and $G$ is a cycle, or $k=3$ and $G$ can be obtained from $K_{3,3}$ and the Heawood graph $H_0$ by repeated star products.

The cited work proved that no such graphs exist for $k\geq 4$ and established additional structural restrictions for $k=3$, but the supplied text gives no resolution of the classification conjecture itself.