Let $G$ be a connected graph with $n$ vertices, and let $m$ be $\min(n-1,2\delta )$ where $\delta$ is the smallest degree of a vertex in $G$. Show that $G$ contains a path that has $m$ edges.
I don't really know how to start. I know that I can always find a path with $\delta$ edges, so many under cetain conditions there is a way to unite two of these paths...?