# uniquely hamiltonian

## Infinite uniquely hamiltonian graphs ★★

Author(s): Mohar

\begin{problem} Are there any uniquely hamiltonian locally finite 1-ended graphs which are regular of degree $r > 2$? \end{problem}

## r-regular graphs are not uniquely hamiltonian. ★★★

Author(s): Sheehan

\begin{conjecture} If $G$ is a finite $r$-regular graph, where $r > 2$, then $G$ is not uniquely hamiltonian. \end{conjecture}

Keywords: hamiltonian; regular; uniquely hamiltonian