Dirac's theorem and Ore's theorem

Two sufficient (not necessary) degree conditions that guarantee a graph is Hamiltonian: Dirac's checks every vertex's own degree, Ore's checks the degree sum of every non-adjacent pair.

Dirac's theorem: if every vertex of a simple graph on $n\ge3$ vertices has degree $\ge n/2$ , the graph is Hamiltonian (theorem: diracs-theorem). Ore's theorem: if $\deg(u)+\deg(v)\ge n$ for every non-adjacent pair $u,v$ , the graph is Hamiltonian (theorem: ores-theorem) -- Dirac's is a direct corollary.