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Exercise 5 Consider a graph G = (V, E), with integer capacities on the edges, such that for all e E \ {e*}, it holds that ce is an even number, and ce is odd. Suppose that there is a maximum flow in this graph with odd flow. a. Prove/Disprove: It must be that in every maximum flow, there is a flow in e* (i.e., fe* > 0). b. Prove/Disprove: It must be that in every maximum flow, there is a full flow in e* (i.e., fe* = Ce*).

Exercise 5 Consider a graph G = (V, E), with integer capacities on the edges, such that for all e E \ {e*}, it holds that ce is an even number, and ce is odd. Suppose that there is a maximum flow in this graph with odd flow. a. Prove/Disprove: It must be that in every maximum flow, there is a flow in e* (i.e., fe* > 0). b. Prove/Disprove: It must be that in every maximum flow, there is a full flow in e* (i.e., fe* = Ce*).

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: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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Exercise 5 Consider a graph G = (V, E), with integer capacities on the edges, such that for all e € E \ {e*}, it holds that ce is an even number, and ce is odd. Suppose that there is a maximum flow in this graph with odd flow. a. Prove/Disprove: It must be that in every maximum flow, there is a flow in e* (i.e., fe* > 0). b. Prove/Disprove: It must be that in every maximum flow, there is a full flow in e* (i.e., fe* = C₂+).
Transcribed Image Text:Exercise 5 Consider a graph G = (V, E), with integer capacities on the edges, such that for all e € E \ {e*}, it holds that ce is an even number, and ce is odd. Suppose that there is a maximum flow in this graph with odd flow. a. Prove/Disprove: It must be that in every maximum flow, there is a flow in e* (i.e., fe* > 0). b. Prove/Disprove: It must be that in every maximum flow, there is a full flow in e* (i.e., fe* = C₂+).
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