Flows and Linear Programming Duality

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In a network with arcs out of the source

s \to a

and ⁠

s \to b

and no arcs into

s

⁠, a flow satisfies

f (s \to a) = 3

and ⁠

f (s \to b) = 2

⁠. What is

∣ f ∣

⁠?

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About these 80 questions

Max-flow min-cut, the algorithms that realise it, and the linear programming duality that explains every min–max theorem here. This set covers the chapter Flows and Linear Programming Duality in Combinatorics: 22 easy, 38 medium and 20 hard questions, each graded instantly with a hint and a full step-by-step solution. Progress is saved in this browser only.

Flow Networks and Feasible Flows — 13 questions
The Max-Flow Min-Cut Theorem — 14 questions
Applications of Max-Flow Min-Cut — 13 questions
The Linear Programming Problem — 13 questions
Duality — 13 questions
Combinatorial Applications of Duality — 14 questions