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Graph TheoryMediumDirected Graphs and Network Flows

Directed Graphs and Network Flows · Medium problem

A flow network has source ss, sink tt, and vertices a,b,ca,b,c, with capacities c(s,a)=7c(s,a)=7, c(s,b)=5c(s,b)=5, c(a,b)=3c(a,b)=3, c(a,c)=5c(a,c)=5, c(b,c)=2c(b,c)=2, c(b,t)=4c(b,t)=4, c(c,t)=7c(c,t)=7. A flow of value 99 is already known to be valid. What is cap⁡(S,T)−9\operatorname{cap}(S,T) - 9 for the cut S={s,a,b}S=\{s,a,b\}, T={c,t}T=\{c,t\}?