A cycle that contains every vertex of a graph $G$ is called a Hamiltonian cycle. A Hamiltonian cycle is a spanning cycle of $G$. A Hamiltonian graph is a graph that contains a Hamiltonian cycle.

A path in a graph that contains every vertex of $G$ is called a Hamiltonian path in $G$. If a graph contains a Hamiltonian cycle, then it also contains a Hamiltonian path. Obviously, removing any edge from a Hamiltonian cycle produces a Hamiltonian path.

• Every complete graph $K_n$ is a Hamiltonian graph.