I'm trying to show that a connected graph which has order >=3, and having the following inequality is Hamiltonian:



```
degG(x) + degG(y) >= n   x and y are two non-adjacent vertices 

```

I know that Dirac's theorem will be helpful here, but I really don't know how to apply it. (Dirac's theorem: Let G be a graph of order n>= 3. If the minimum degree of graph G is >= n/2, then G is Hamiltonian).


Could you guys give me any hints? Thanks! 



degG(x) + degG(y) >= n, show that the graph is hamiltonian
Your result is true. It is a generalization of Dirac's Theorem known as [Ore's Theorem](https://en.wikipedia.org/wiki/Ore%27s_theorem).


