Discrete Mathematics with Graph Theory (3rd Edition) 392

# Discrete Mathematics with Graph Theory (3rd Edition) 392 -...

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390 3. [BB] The needs of the retail outlets cannot be met. They can receive at most 14 units a month, as shown. To see that the flow S there is a maximum, consider the cut in which T = {a, F, G, t} and S is the set of all other vertices. 4. Now the retail outlets can receive at most 13 units. To see that the flow shown is maximum, consider the cut in which T = S {a, F, G, t} and S is the set of all other ver- tices. Solutions to Exercises 5. (a) [BB] A maximum flow is shown on the left, with directions added to the undirected edges. 1 1 S t 4,3 (b) A maximum flow is shown on the right, with directions added. 6. The maximum number of edge disjoint paths from s to t is three: Observe that sdct, sabt, and sfet are three edge disjoint paths from s to t and no more than three such paths can be found. The minimum number of edges whose removal severs all paths from s to t is three: If fewer than three edges incident with s are not removed, then a path remains. 7. [BB] Four messengers can be sent.
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## This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

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