Max-flow Min-cut Theorem

This lecture covers the fundamental concept that the maximum flow in a network is equal to the minimum cut, exploring applications of flows, net flow across a cut, capacity of a cut, and edge-disjoint paths. The instructor explains the equivalence between a maximum flow, the absence of augmenting paths, and the flow value across a minimum cut. Through examples and proofs, the lecture demonstrates how to find the maximum flow by identifying augmenting paths and computing bottlenecks. Additionally, it discusses the significance of edge-disjoint paths in scenarios like traveling from Lausanne to Geneva airport in winter. The lecture concludes by highlighting the relationship between max-flow and edge-disjoint paths, emphasizing the importance of understanding flow conservation and cut capacities.