# properties of the Greedy Algorithm (Graph Colouring)

So I have shown, that for all n $\in N$ there is a graph $G$ with n vertices such that the Greedy Algorithm will colour it in exactly 2 colours.

Further I have shown that for a Graph with diameter at least 3 there is an ordering of the vertices such that the Greedy Algorithm uses at least 3 colours. (both rather trivial tasks admittedly.)

Apparently these 2 rather basic insights should give me some more interesting property though, and I m wondering what that could be.

-
There's really no need to use the symbols $\forall, \exists$ when ordinary English would be much more readable. – Qiaochu Yuan Feb 7 '12 at 23:29