Discrete Mathematics with Graph Theory (3rd Edition) 390

Discrete Mathematics with Graph Theory (3rd Edition) 390 -...

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388 Solutions to Exercises 3. (a) [BB] To see that the pictured flow is maximum, consider the cut S = {s, b}, T = {a,c,d,e,f,t}. (b) To see that the pictured flow is maximum, consider the cut S = {s,a,c,d,e}, T = {b,f,t}. (c) [BB] To see that the pictured flow is maximum, consider the cut S = {s,b}, T = {a,c,d,e,f,g,h,t}. (d) To see that the pictured flow is maximum, consider the cut S = {s,a}, T = {b, c, d, e, f, g, h, i, t}. (e) To see that the pictured flow is maximum, consider
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Unformatted text preview: the cutS = {s,a, b,c,d, e, f,g, h, i}, T={j,t}. a s c s a s c a 7,4 c 11,4 e s t b 3,3 d 12,6 f 6,6 d t 2,2 f a 4,3 9 t c h 8,6 h t 6,6 4. (a) [BB] We multiply the capacities by 10, the greatest common divisor of the denominators, and find a maximum flow in the new network, as shown on the left. Then, dividing by 10, we find a maximum flow in the given network, of value ~b' as shown on the right. (Only the flow in each arc is shown.)...
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