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Recall that a trail is a walk that does not contain a repeated edge, a closed...

  1. Recall that a trail is a walk that does not contain a repeated edge, a closed trail is a trail whose initial and terminal vertices are the same, a non-trivial walk contains at least one edge, and a cycle is a closed trail where the only repeated vertex is the terminal vertex repeating the initial vertex. Prove that every non-trivial closed trail contains a cycle.
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