Maximum Flow: Theory and Applications

This lecture covers the concept of maximum flow in graphs, discussing the Ford-Fulkerson algorithm, flow conservation, capacity constraints, and the notion of minimum cut. The instructor explains how to determine the maximum flow in a network by constructing a partition of vertices reachable from the source. Through examples and demonstrations, the lecture illustrates how to identify the minimum cut that corresponds to the maximum flow, emphasizing the importance of flow conservation and capacity limitations. The instructor also introduces the concept of residual graphs and demonstrates how to use them to find the maximum flow in a network. The lecture concludes with exercises for students to practice applying the theoretical concepts discussed.