Prove that every connected graph has a vertex whose removal (including all adjacent edges) will not disconnect the graph, and write a DFS method that finds such a vertex.

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Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.