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
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