Sheehan's conjecture on 2-factor Hamiltonian regular bipartite graphs

Let $G$ be a $2$-factor Hamiltonian $k$-regular bipartite graph, meaning that every $2$-factor of $G$ is a Hamiltonian circuit. Sheehan's conjecture. There are no $2$-factor Hamiltonian $k$-regular bipartite graphs for any integer $k\geq 4$. This is the higher-degree exclusion suggested by the classification conjecture above and remains open in the survey.