English: A graph illustrating Ore's theorem, that when all pairs of nonadjacent vertices have degrees summing to at least n, the graph has a Hamiltonian cycle. Here, the two degree-three vertices in the center are adjacent, and all other pairs of vertices have degrees summing to at least seven, the number of vertices. Because some vertices have fewer than n/2 neighbors, the conditions for the weaker Dirac theorem on Hamiltonian cycles are not met. A Hamiltonian cycle is highlighted.