A simple graph with 
graph vertices in which
each graph vertex has vertex
degree 
has a Hamiltonian cycle.
Dirac's Theorem
See also
Hamiltonian CycleExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Dirac's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DiracsTheorem.html