I have the following exercise to do but don't know how to approach it:
Let $G$ be a graph with $n$ nodes ($n \ge 2$), and where every node has degree at least $3$. Show that $G$ has a cycle of length $\le 2\cdot \lceil\log n\rceil$. And it allows me to consider a breadth-first search tree.
First of all, what's the length of a cycle? Is it the number of arcs in the cycle? Secondly, how do I show it's $2\cdot\lceil\log n\rceil$?
Thanks, Sorin