title: Is every bridge in a graph an edge in DFS search tree?
body: <p>A question from Skiena's book of algorithm:</p>
  
  <p>Suppose G is a connected undirected graph. An edge e whose removal disconnects
  the graph is called a bridge. Must every bridge e be an edge in a depth-first search tree of G?</p>
  
  <p>My solution so far (need suggestions):</p>
  
  <p>I think that the bridge is an edge whose end vertex is a cut node, because cut node removal disconnects the graph so removing that edge will also disconnect the graph. Edges in DFS search tree are tree edges &amp; back edges, and only tree edges can be cut edges ( or bridges ) because back edge removal doesn't disconnect the graph.</p>