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