Graph Theory Questions Medium
The bipartite matching problem in graph theory refers to finding a maximum matching in a bipartite graph. A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that there are no edges between vertices within the same set. In other words, the graph can be represented as two sets of vertices, with edges only connecting vertices from different sets.
The bipartite matching problem aims to find a matching, which is a subset of edges in the graph such that no two edges share a common vertex. A maximum matching is a matching that contains the maximum possible number of edges.
The problem can be solved using various algorithms, such as the Hopcroft-Karp algorithm or the Ford-Fulkerson algorithm. These algorithms aim to find the maximum matching by iteratively augmenting the matching until no more augmenting paths can be found.
Bipartite matching has numerous applications in various fields, including computer science, operations research, and economics. It can be used to solve problems like assigning tasks to workers, matching students to schools, or pairing buyers and sellers in a market.