title: Maximal Spanning Tree to find a minimal set of edges that cover each cycle
body: <p>I got the following task: Given a graph G := (V, E) with arbitrarily many cycles. What is the minimal set of edges so that for every cycle in the graph at least one edge is included in the set - or to be more precise, what is the sum of the weight of those edges.</p>
  
  <p>My approach was pretty straight forward: I computed a maximum spanning forest over the graph, excluded each edge and proclaimed the remaing edges as result. The idea goes as follows: Since each spanning tree has no cycles I will never remove an entire cycle and thus there will not be any cycles I did not cover. Furthermore I also would not be able to remove any other edge in the graph G since if I did I would remove a cycle and thus the result would not cover all cycles. Thus I concluded my method would be correct.</p>
  
  <p>However it seems that this is not the case. Can anybody enligthen me where I went wrong? I could not come up with an example that disproves my method.</p>