Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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Theorem 3.1.2. Let x be a edge of a connected graph G. The following statements
are equivalent:
(1) x is a bridge of G.
(2) x is not on any cycle of G.
(3) There exist vertices u and v of G such that the edge x is on every path joining u and
v.
(4) There exists a partition of V into subsets U and W such that for any vertices
u E U and w E W the edge x is on every path joining u and w.
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Transcribed Image Text:Theorem 3.1.2. Let x be a edge of a connected graph G. The following statements are equivalent: (1) x is a bridge of G. (2) x is not on any cycle of G. (3) There exist vertices u and v of G such that the edge x is on every path joining u and v. (4) There exists a partition of V into subsets U and W such that for any vertices u E U and w E W the edge x is on every path joining u and w.
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