Let (u, v) be a directed edge in arbitrary flow network G. Prove that if there is a minimum (s, t)-cut (S, T) such that u ∈ S and v ∈ T, then there is no minimum cut (S', T' ) such that u ∈ T' , v ∈ S' ). Note that by definition of cut, s ∈ S, t ∈ T, and similarly s ∈ S' , t ∈ T'.
Let (u, v) be a directed edge in arbitrary flow network G. Prove that if there is a minimum (s, t)-cut (S, T) such that u ∈ S and v ∈ T, then there is no minimum cut (S', T' ) such that u ∈ T' , v ∈ S' ). Note that by definition of cut, s ∈ S, t ∈ T, and similarly s ∈ S' , t ∈ T'.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Let (u, v) be a directed edge in arbitrary flow network G. Prove that if there is a minimum (s, t)-cut (S, T) such that u ∈ S and v ∈ T, then there is no minimum cut (S', T' ) such that u ∈ T' , v ∈ S' ). Note that by definition of cut, s ∈ S, t ∈ T, and similarly s ∈ S' , t ∈ T'.
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