Abreu–Aldred–Funk–Jackson–Sheehan conjecture on 4-regular non-bipartite graphs

Let $K_5$ denote the complete graph on five vertices, and let a graph be 2-factor Hamiltonian when every $2$-factor is a Hamiltonian circuit. Abreu–Aldred–Funk–Jackson–Sheehan's conjecture. The graph $K_5$ is the only 2-factor Hamiltonian 4-regular non-bipartite graph. The survey presents this as an open conjecture and denotes the corresponding class by $HU(4)=\{K_5\}$.