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In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink is equal to the total weight of the edges in a minimum cut, i.e., the smallest total weight of the edges which if removed would disconnect the source from the sink. This is a special case of the duality theorem for linear programs and can be used to derive Menger's theorem and the Kőnig–Egerváry theorem.

Approximate max-flow min-cut theorem - Approximate max-flow min-cut theorems are mathematical propositions in network flow theory. Approximate max-flow min-cut theorems deal with the relationship between maximum flow rate and minimum cut in a multi-commodity flow problem.

Flow network - In graph theory, a flow network is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge.

GNRS conjecture - In theoretical computer science and metric geometry, the GNRS conjecture connects the theory of graph minors, the stretch factor of embeddings, and the approximation ratio of multi-commodity flow problems.

Linear programming - Linear programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming.

Maximum flow - In optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem.

Menger's theorem - In the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number of disjoint paths that can be found between any pair of vertices. Proved by Karl Menger in 1927, it characterizes the connectivity of a graph.

Theorems in graph theory

Combinatorial optimization