WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »
Combinatorica`
Combinatorica`

BipartiteMatchingAndCover

As of Version 10, most of the functionality of the Combinatorica package is built into the Wolfram System. »

BipartiteMatchingAndCover[g]

takes a bipartite graph g and returns a matching with maximum weight along with the dual vertex cover. If the graph is not weighted, it is assumed that all edge weights are 1.

Details and Options

Examples

Basic Examples  (2)Summary of the most common use cases

In[1]:=1
✖
https://wolfram.com/xid/0jevd2slv1ebadtref3wki-rmcvi
In[2]:=2
✖
https://wolfram.com/xid/0jevd2slv1ebadtref3wki-euxtzb
In[3]:=3
✖
https://wolfram.com/xid/0jevd2slv1ebadtref3wki-c7xwog
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0jevd2slv1ebadtref3wki-fczqlq
Out[4]=4

BipartiteMatchingAndCover has been superseded by FindIndependentEdgeSet:

In[1]:=1
✖
https://wolfram.com/xid/0jevd2slv1ebadtref3wki-ec1xd2
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jevd2slv1ebadtref3wki-q4ahb
Out[2]=2
Wolfram Research (2012), BipartiteMatchingAndCover, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html.
✖
Wolfram Research (2012), BipartiteMatchingAndCover, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html.

Text

Wolfram Research (2012), BipartiteMatchingAndCover, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html.

✖
Wolfram Research (2012), BipartiteMatchingAndCover, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html.

CMS

Wolfram Language. 2012. "BipartiteMatchingAndCover." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html.

✖
Wolfram Language. 2012. "BipartiteMatchingAndCover." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html.

APA

Wolfram Language. (2012). BipartiteMatchingAndCover. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html

✖
Wolfram Language. (2012). BipartiteMatchingAndCover. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html

BibTeX

@misc{reference.wolfram_2025_bipartitematchingandcover, author="Wolfram Research", title="{BipartiteMatchingAndCover}", year="2012", howpublished="\url{https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html}", note=[Accessed: 03-April-2025 ]}

✖
@misc{reference.wolfram_2025_bipartitematchingandcover, author="Wolfram Research", title="{BipartiteMatchingAndCover}", year="2012", howpublished="\url{https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html}", note=[Accessed: 03-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_bipartitematchingandcover, organization={Wolfram Research}, title={BipartiteMatchingAndCover}, year={2012}, url={https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html}, note=[Accessed: 03-April-2025 ]}

✖
@online{reference.wolfram_2025_bipartitematchingandcover, organization={Wolfram Research}, title={BipartiteMatchingAndCover}, year={2012}, url={https://reference.wolfram.com/language/Combinatorica/ref/BipartiteMatchingAndCover.html}, note=[Accessed: 03-April-2025 ]}