# line graphs

## Hamiltonian cycles in line graphs of infinite graphs ★★

Author(s): Georgakopoulos

\begin{conjecture} \begin{enumerate} \item If $G$ is a 4-edge-connected locally finite graph, then its \Def{line graph} is hamiltonian. \item If the line graph $L(G)$ of a locally finite graph $G$ is 4-connected, then $L(G)$ is hamiltonian. \end{enumerate} \end{conjecture}

Keywords: hamiltonian; infinite graph; line graphs

## Hamiltonian cycles in line graphs ★★★

Author(s): Thomassen

\begin{conjecture} Every 4-connected \Def{line graph} is \Def[hamiltonian]{Hamilton cycle}. \end{conjecture}

Keywords: hamiltonian; line graphs