Dirac 1952: a simple graph on n ≥ 3 vertices with minimum degree at least n/2 contains a Hamilton cycle. Sharp at C_n for n = 4. Ore's theorem generalises to 'deg(u) + deg(v) ≥ n for every non-adjacent pair'.
Dirac 1952: a simple graph on n ≥ 3 vertices with minimum degree at least n/2 contains a Hamilton cycle. Sharp at C_n for n = 4. Ore's theorem generalises to 'deg(u) + deg(v) ≥ n for every non-adjacent pair'.