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.)
Aggregate parent (I am a part of or used in ...)
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 (email@example.com) 5 Sep 1999.
If you have suggestions, corrections, or comments, please get in touch with Paul Black.
Entry modified 17 December 2004.
HTML page formatted Wed Mar 13 12:42:46 2019.
Cite this as:
Paul E. Black, "perfect matching", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 17 December 2004. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/perfectmatch.html