Do connected graphs with more than N-1 edges always contain connected graph with N-1 edges?
<p>We know that:</p>

<p>If we have N vertices
To build a connected undirected graph, you'll need at least N-1 edges.
Let M be the set of possible connected undirected graphs with N-1 edges.</p>

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<p>Can we prove or disprove that if there's an undirected connected graph with more than N-1 edges, it must contain one of the graphs in M?  In other words, can we take one of the graphs in M and add edges to create this new graph?  </p>

<p>(by "containing", I mean that it has all the edges of the other graph plus some more.)</p>