Discrete Mathematics with Graph Theory (3rd Edition) 388

# Discrete Mathematics with Graph Theory (3rd Edition) 388 -...

This preview shows page 1. Sign up to view the full content.

386 Solutions to Exercises Exercises 14.2 1. (a) i. [BB] One flow-augmenting chain is sbadt in which the slack is 1. ii. [BB] Here is a maximum flow, of value 7. We can see this is maximum by examining the cut S = {s,a,b}, T = {c,d,e,/,t}, of capacity C sc + Cad + Cbe = 3 + 3 + 1 = 7, the value of the flow. d f (b) i. One flow-augmenting chain is sadt, with slack 1. Another is sadcbt, also with slack 1. a 2,2 b ii. We show a maximum flow, of value 9. We can see that this is maximum by examining t s G-~~--~~~----~----~ the cut S = {s}, T = {a,b,c,d,e,t} which has capacity C sa + C se + C sc = 4 + 3 + 2 = 9, the value of the flow. c 1,0 d t (c) i. One flow-augmenting chain is sagt, which has slack
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: sabce / gt, which has slack 1 as well. 11. We show a maximum flow, of value 8. We can see this is maximum by examining the cut s S = {s,a,b,c,e,/,g}, T = {d,t} which has capacity Ccd + Cfd + Cgt = 5 + 1 + 2, the value of the flow. (d) i. [BB] One flow-augmenting chain is saed/gt, which has slack 1. ii. [BB] We show a maximum flow, of value 20. We can see this is maximum by examining the cutS = {s,a,b,c}, T = {d,e,/,g,h,t}. This has capacity Cse+Csh +Ccd = 7+4+9 = 20, the value of the flow. a sCf-~---if-____ ""--"'--+--+--~t e 6,6 f 7,7 9 (e) 1. One flow-augmenting chain is sacghkt in which the slack is 4. ii. We show a maximum flow, of value 13. t...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern