Sheehan's uniquely Hamiltonian regular graph conjecture

Let $G$ be a finite simple $k$-regular graph, where a graph is uniquely Hamiltonian if it has exactly one Hamiltonian circuit. Sheehan's conjecture. There are no uniquely Hamiltonian $k$-regular graphs for any integer $k\geq 3$. This extends the parity obstruction for odd-regular multigraphs and remains open for general regular graphs of degree at least three.