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The chapter introduces the concept of bipartite graphs and their application in job assignment problems. It explains various types of matchings, such as maximum, maximal, and complete matching, along with a necessary condition for the existence of a complete matching in bipartite graphs as elucidated by Hall's marriage theorem. Through examples, the chapter illustrates how these concepts can help in modeling assignments fairly and effectively in different organizational setups.
Chapter 2512 sections
The chapter introduces the concept of bipartite graphs and their application in job assignment problems. It explains various types of matchings, such as maximum, maximal, and complete matching, along with a necessary condition for the existence of a complete matching in bipartite graphs as elucidated by Hall's marriage theorem. Through examples, the chapter illustrates how these concepts can help in modeling assignments fairly and effectively in different organizational setups.
Bipartite graphs can be used to model job assignments between two sets of entities.
A matching in a graph helps ensure that certain conditions, such as employees not being assigned multiple jobs, are met.
Hall's marriage theorem provides a necessary and sufficient condition for the existence of complete matching in bipartite graphs.
A graph whose vertices can be divided into two disjoint sets such that no two graph vertices within the same set are adjacent.
A set of edges in a graph such that no two edges share a vertex.
A matching that contains the largest possible number of edges.
A matching that cannot be extended by adding an edge.
A matching where every vertex in one set is matched with a vertex in the other set.
A condition that must be satisfied for a complete matching to exist in a bipartite graph, stating that for any subset of vertices the number of neighbors must be greater than or equal to the number of vertices in the subset.
Total Questions
2
Estimated Time
4 min
Passing Score
70%
1 more question available