BUILT-IN MATHEMATICA SYMBOL

FindIndependentEdgeSet

FindIndependentEdgeSet[g]
finds an independent edge set of the graph g with a maximum number of edges.

MORE INFORMATION

FindIndependentEdgeSet returns a list of edges.

An independent edge set is a set of edges that are never incident to the same vertex.

An independent edge set is also known as a matching.

EXAMPLES

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Basic Examples (2)

Find an independent edge set in a complete graph:

In a directed graph:

Find an independent edge set in a complete graph:

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In a directed graph:

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Scope (2)

FindIndependentEdgeSet works with undirected graphs:

Directed graphs:

Applications (3)

A company has a number of different jobs. Each employee is suited for some of these jobs, and each person can perform at most one job at a time:

Maximize the number of jobs that can be performed simultaneously:

Given a set of women, each of whom has a preference for some subset of men, find a maximal matching where only matches that agree with preferences are allowed:

Compute a maximal matching:

An art history department would like to offer six courses. There are eight professors, each of whom is willing to teach certain courses. Find a maximal matching where professors only teach courses they are interested in teaching:

Match preferences to courses:

Properties & Relations (3)

Test whether a set of edges is an independent edge set using IndependentEdgeSetQ:

Bipartite graphs have independent edge sets and vertex covers of equal length:

For a graph without isolated vertices, the sum of the size of the independent edge set and the size of the edge cover is equal to the number of vertices: