Which of these is the correct condition for a graph to be Hamiltonian?
Dirac's Theorem: If deg(v)≥n/2\deg(v) \geq n/2deg(v)≥n/2 for all vvv, then GGG is Hamiltonian.
Ore's Theorem: If deg(u)+deg(v)≥n\deg(u) + \deg(v) \geq ndeg(u)+deg(v)≥n for all non-adjacent u,vu, vu,v, then GGG is Hamiltonian.
The graph must be a tree.
The graph must be bipartite.