Yeas all the options are true, in fact some of this are well known theorems
Dirac's Theorem:
if G is a simple graph of n vertices ,where n>=3 ,such that the every vertex of G has a degree at least n/2 ,is a hamiltonian circuit
Ore's Theorem:
if G is a simple graph of n vertices ,where n>=3 such that deg(u)+deg(v)>=n for every pair of NONADJACENT vertices u,v in the graph..then G has a Hamiltonian CKt
Another theorem:
A vertices with no loop and paralle edges, which has atleast 1/2(n-1)(n-2)+2 edge ,is Hamiltonian
refer:http://mathonline.wikidot.com/dirac-s-and-ore-s-theorem
so i think all are true