As I understand a graph has a Hamilton Circuit if
- It has $n \ge 3$ vertexes
- degree of every vertex is at least $n/2$
- $\deg u + \deg v \ge n$ for every pair of nonadjacent vertices $u$ and $v$ in the graph
I can't seem to find a concrete set of properties for deciding if a graph has a Hamilton Path. Can anyone help me out? Please add some references/sources :)