GRAPH UTILITIES PACKAGE SYMBOL

MaximalBipartiteMatching

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

DetailsDetails

• To use , you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
• gives a maximal set of nonadjacent edges between the two vertex sets of the bipartite graph.
• The bipartite graph represented by an matrix consists of the row and column vertex sets and C={1, 2, ..., n}, with a vertex iR and jC connected if the matrix element .
• The bipartite graph represented by a rule list consists of vertex sets R=Union[{i1, i2, ...}] and C=Union[{j1, j2, ...}], with a vertex iR and jC connected if the rule is included in the rule list.
• returns a list of index pairs , where the number of pairs k is not larger than either vertex set.

ExamplesExamplesopen allclose all

Basic Examples (1)Basic Examples (1)

A bipartite graph describing acceptable drinks for four people:

The drink each person should have, if no two people are to have the same drink:

 Out[3]=