1. ## Hamiltonian circuits

Hi guys.

Im trying to solve this problem with Hamiltonian circuits.
"Show that all simple, complete graphs with at least three vertices has an hamiltonian circuit"

My problem is that Im not sure how to "show" this. It is easy to draw a graph with, say, 7 vertices and point out a circuit, but that doesnt show anything else than that specific graph has a circuit.

Any thoughts?

2. Think DIRAC'S.
Is it true that if $n\ge 3$ then $n-1\ge \frac{n}{2}?$