Unformatted text preview: S = {s, a, b, e, d, e, J}, T = {t}. (c) i. Send one unit through selt. ii. Send four units through selt, saturating se and ef. iii. Here is a maximum flow, of value 9. (Did you get it?) s b 2,2 d c 4,4 f To see that this is maximum, consider the cut S = {s, a}, T = {b, e, d, e, I, t}. (d) i. Send one unit through the path set. ii. Send two units through set, saturating et. iii. Here is a maximum flow, of value 10. (Did you get it?) d e To see that the flow is maximum, consider the cut S = {s, a, b, e, d, e}, T = {t}. b 6. [BB] s 1,0 a t c d t f t t 7. [BB] Let {Sl, 7i} be any cut. By Theorem 14.1.4, val(F) ~ cap(Sl, 7i). But val(F) = cap(S, T). So cap( S, T) ~ cap( Sl, 7i). Since {Sl, 7i} was an arbitrary cut, the result is proven....
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 Summer '10
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 Graph Theory, Trigraph, maximum flow

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