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.
$
C = {v_0, v_1, v_3, v_8, v_{12}, v_{13}, v_9, v_4, v_5, v_6, v_{10}, v_{14}, v_{11}, v_7, v_2, v_0}
$
- Every complete graph $K_n$ is a Hamiltonian graph.
