Aldred–Funk–Jackson–Labbate–Sheehan conjecture on 2-factor isomorphic graphs

Let $G$ be a connected $k$-regular bipartite graph. A graph is 2-factor isomorphic when all its $2$-factors are isomorphic, and it is 2-factor Hamiltonian when every $2$-factor is a Hamiltonian circuit. Aldred–Funk–Jackson–Labbate–Sheehan's conjecture. The graph $G$ is $2$-factor isomorphic if and only if it is $2$-factor Hamiltonian. The survey notes that this unrestricted form is false, through a construction of non-Hamiltonian connected $2$-factor isomorphic cubic bipartite graphs.