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side. Consider the directed bipartite graph Km,n where all edges go from the m side to the n Introduce a new vertex s and edges from it to the m side. Similarly, introduce t and edges to it from the n side. Give all the edges capacity 1, making this a flow network G with vertex set V and edges set E. m (a) Naively, what is the maximum flow on this network? (b) Assuming m≤n, describe a (simple) min cut. (c) Assuming m≥n, describe a min cut.

side. Consider the directed bipartite graph Km,n where all edges go from the m side to the n Introduce a new vertex s and edges from it to the m side. Similarly, introduce t and edges to it from the n side. Give all the edges capacity 1, making this a flow network G with vertex set V and edges set E. m (a) Naively, what is the maximum flow on this network? (b) Assuming m≤n, describe a (simple) min cut. (c) Assuming m≥n, describe a min cut.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the directed bipartite graph Km,n where all edges go from the m side to the n side. Introduce a new vertex s and edges from it to the m side. Similarly, introduce t and edges to it from the n side. Give all the edges capacity 1, making this a flow network G with vertex set V and edges set E. m (a) Naively, what is the maximum flow on this network? (b) Assuming m≤n, describe a (simple) min cut. (c) Assuming m≥n, describe a min cut. n C
Transcribed Image Text:Consider the directed bipartite graph Km,n where all edges go from the m side to the n side. Introduce a new vertex s and edges from it to the m side. Similarly, introduce t and edges to it from the n side. Give all the edges capacity 1, making this a flow network G with vertex set V and edges set E. m (a) Naively, what is the maximum flow on this network? (b) Assuming m≤n, describe a (simple) min cut. (c) Assuming m≥n, describe a min cut. n C
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