Show that from a simple connected undirected graph on $n$ vertices and having $m$ edges, one can always pick $m-n+1$ edges in such a way that at least one edge is picked from every cycle in the graph.
This question I have faced during my preparation for M.Tech.I have tried a lot but have no idea, how to go further.Please if possible help me to solve this question. I think connected graph results and Pigeon-hole Principle can help me to solve.
My attempt, Since the graph is connected, $m \geq n -1$ as $\omega(G)=1 $. This implies $m-n+1 \geq 0$.
Next how can I move ?