MaximalBipartiteMatching

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. >>

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

DetailsDetails

  • MaximalBipartiteMatching functionality is now available in the built-in Wolfram Language function FindIndependentEdgeSet.
  • 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  (2)Basic Examples  (2)

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A bipartite graph describing acceptable drinks for four people:

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

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has been superseded by FindIndependentEdgeSet:

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