How can I prove that G/e is connected? (If G is a connected graph and e is an edge of G) And what does a spanning tree has to do with this proof?

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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.