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?

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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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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In part 4. you're talking about removing e which gives us then two connected compoments. But in this example (G/e) we have to contract e and not removing it?

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