Minimum Vertex Cover in Bipartite Graphs with Ford-Fulkerson

Graph theory problems can seem abstract and difficult to solve without the right algorithmic framework. Understanding how to transform a complex graph problem into a network flow problem is a fundamental skill for any programmer or computer science student. This text-only course guides you through the process of finding a minimum vertex cover in bipartite graphs. By connecting Konig's theorem with the Ford-Fulkerson algorithm, you will gain a clear, mathematical, and practical understanding of how network flows solve classic graph optimization problems. What you'll learn: Understand the fundamental concepts of bipartite graphs, independent sets, and vertex covers; Apply Konig's theorem to establish the mathematical link between maximum matchings and minimum vertex covers; Formulate bipartite matching problems as network flow networks with source and sink nodes; Execute the Ford-Fulkerson algorithm step-by-step to find maximum flows and minimum cuts; Construct the actual minimum vertex cover set from the residual graph; Analyze the time complexity and edge cases of these algorithms using clean, modern code representations. We begin with core definitions of graph theory before moving through the network flow transformation. You will then work through detailed, text-based walkthroughs and written exercises to solidify your understanding of the algorithm. This course is designed for beginners who want to strengthen their algorithmic problem-solving skills, with no advanced prerequisites required. Start reading today to master the intersection of network flows and graph optimization.