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Graph Utilities Package Symbol

MaximalBipartiteMatching

MaximalBipartiteMatching[g]
gives the maximal matching of the bipartite graph g.

To use MaximalBipartiteMatching, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].

MaximalBipartiteMatching gives a maximal set of non-adjacent edges between the two vertex sets of the bipartite graph.

The bipartite graph represented by an m×n matrix consists of the row and column vertex sets R={1, 2, ..., m} and C={1, 2, ..., n}, with a vertex iR and jC connected if the matrix element g_ij≠0.

The bipartite graph represented by a rule list {i₁->j₁, i₂->j₂, ...} consists of vertex sets R=Union[{i₁, i₂, ...}] and C=Union[{j₁, j₂, ...}], with a vertex iR and jC connected if the rule i->j is included in the rule list.

MaximalBipartiteMatching returns a list of index pairs {{i₁, j₁}, ..., {i_k, j_k}} where the number of pairs k is not larger than either vertex set.

Needs["GraphUtilities`"]

A bipartite graph describing acceptable drinks for 4 people:

The drinks each person should have, if no two person is to have the same drink: