A trail is a walk that does not repeat an edge. Prove that a trail that repeats a vertex must contain a cycle. (Think about the set of nontrivial sub-walks along the trail that start and end at the same vertex.)

A trail is a walk that does not repeat an edge. Prove that a trail that repeats a vertex must contain a cycle. (Think about the set of nontrivial sub-walks along the trail that start and end at the same vertex.)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.5: The Format Proof Of A Theorem

Problem 12E: Based upon the hypothesis of a theorem, do the drawings of different students have to be identical...

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Question

A trail is a walk that does not repeat an edge. Prove that a trail that
repeats a vertex must contain a cycle. (Think about the set of
nontrivial sub-walks along the trail that start and end at the same
vertex.)

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