Consider the directed network (D, c) given by the following drawing, where each arc e E A(D) is labelled by its capacity c(e). 3 Let f A(D) R with 2 V2 33 03 201 4 1 2 4 1 2 4 2 3 U6 UA U5 1 f(v1v2) = 2, f(v₁₁) = 1, f(v2v5) = 0, f(v2v6) = 3, f(v3v1) = 1, f(v3v2) = 2, f(u422) = 1, f(v4v5) = 0, f(v4v6) = 0, f("501) = 1, f(v5v3) = 1, f(v6v1) = 1, f(v6v3) = 2, f(v6v5) = 2. (a) Give s, tЄ V(D) such that f is an s-t-flow of (D, c) and has positive size. For this you may want to consider, for each vertex v EV(D), the overall amount of flow on arcs with head v and the overall amount of flow on arcs with tail v. Explain why f is an s-t-flow and give its size. (b) Find a maximum s-t-flow of (D, c). Show your working. (c) Use a cut to show that the flow you have found is indeed a maximum s-t-flow of (D, c).

Consider the directed network (D, c) given by the following drawing, where each arc e E A(D) is labelled by its capacity c(e). 3 Let f A(D) R with 2 V2 33 03 201 4 1 2 4 1 2 4 2 3 U6 UA U5 1 f(v1v2) = 2, f(v₁₁) = 1, f(v2v5) = 0, f(v2v6) = 3, f(v3v1) = 1, f(v3v2) = 2, f(u422) = 1, f(v4v5) = 0, f(v4v6) = 0, f("501) = 1, f(v5v3) = 1, f(v6v1) = 1, f(v6v3) = 2, f(v6v5) = 2. (a) Give s, tЄ V(D) such that f is an s-t-flow of (D, c) and has positive size. For this you may want to consider, for each vertex v EV(D), the overall amount of flow on arcs with head v and the overall amount of flow on arcs with tail v. Explain why f is an s-t-flow and give its size. (b) Find a maximum s-t-flow of (D, c). Show your working. (c) Use a cut to show that the flow you have found is indeed a maximum s-t-flow of (D, c).

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

Section1.1: Early Definitions And Postulates

Problem 36E: Consider noncoplanar points A, B, C, and D. Using three points at a time such as A, B, and C, how...

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