NIST

perfect matching

(definition)

Definition: A matching, or subset of edges without common vertices, of a connected graph that touches all vertices exactly once. A graph with an odd number of vertices is allowed one unmatched vertex.

Specialization (... is a kind of me.)
bipartite matching.

Aggregate parent (I am a part of or used in ...)
Christofides algorithm.

Note: The term comes from matching each vertex with exactly one other vertex.

Any perfect matching of a graph with n vertices has n/2 edges.

If a graph has a Hamiltonian cycle, it has two different perfect matchings, since the edges in the cycle could be alternately colored. After Douglas Bass (dbass@stthomas.edu) 5 Sep 1999.

Author: PEB


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Entry modified 17 December 2004.
HTML page formatted Fri Feb 23 10:06:08 2018.

Cite this as:
Paul E. Black, "perfect matching", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/perfectmatch.html