
A matching, also called an independent edge phối, on a graph


Bạn đang xem: Matching
It is not possible for a matching on a graph with



While not all graphs have perfect matchings, a largest matching (commonly known as a maximum matching or maximum independent edge set) exists for every graph. The kích thước of this maximum matching is called the matching number of


The number of matchings in a graph is sometimes called the Hosoyaindex.
A maximal independent edge mix, which is different from a maximum independent edge set, is a matching that cannot be enlarged by simply adding an edge. Such matchings are easy khổng lồ compute, but are not necessarily maximum independent edge sets. A maximal independent edge set on a general graph can be found using MaximalMatching
The blossom algorithm can be used lớn find a maximum independent edge mix in a general graph, while the simpler Hungarian maximum matching algorithm can be used for bipartite graphs. A maximum independent edge mix can be computed in the cheap-kenya-vacation-tips.com Language using FindIndependentEdgeSet
Let the number of distinct







The matching polynomial is defined by
![]() |
và the matching-generating polynomialby
![]() |
The numbers of distinct





graph | ![]() |
complete graph ![]() | ![]() |
complete bipartite graph ![]() | ![]() |
cycle graph ![]() | ![]() |
empty graph ![]() | ![]() |
path graph ![]() | ![]() |
SEE ALSO: Berge"s Theorem, Blossom Algorithm, Hosoya Index, Hungarian Maximum Matching Algorithm, Independent Edge Set, Marriage Theorem, Matching-Generating Polynomial, Matching Number, Matching Polynomial, Maximal Independent Edge Set, Maximum Independent Edge Set, Near-Perfect Matching, Perfect Matching, Stable Marriage Problem
REFERENCES:
Hopcroft, J. & Karp, R. "An

Lovász, L. và Plummer, M.D. MatchingTheory. Amsterdam, Netherlands: North-Holl&, 1986.
Pemmaraju, S. and Skiemãng cầu, S. "Matching." §8.4 in Computational Discrete Mathematics: Combinatorics and Graph Theory in Mathematica. Cambridge, England: Cambridge University Press, pp.343-351, 2003.
Xem thêm: Công An Thành Phố Hồ Chí Minh Tiếng Anh Là Gì, Từ Vựng Tiếng Anh Về Thành Phố
Skiemãng cầu, S. "Matching." §6.4 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp.240-246, 1990.
Zwiông xã, U. "Lecture Notes on: Maximum Matching in Bipartite and Non-BipartiteGraphs." 2009. https://www.cs.tau.ac.il/~zwick/grad-algo-0910/match.pdf.
Referenced on cheap-kenya-vacation-tips.com|Alpha: Matching
CITE THIS AS:
Weisstein, Eric W. "Matching." From cheap-kenya-vacation-tips.com--A cheap-kenya-vacation-tips.com Web Resource. https://cheap-kenya-vacation-tips.com/Matching.html
cheap-kenya-vacation-tips.com Web Resources
Mathematica» The #1 tool for creating Demonstrations & anything technical. | cheap-kenya-vacation-tips.com|Alpha» Explore anything with the first computational knowledge engine. | cheap-kenya-vacation-tips.com Demonstrations Project» Explore thousands of miễn phí applications across science, mathematics, engineering, giải pháp công nghệ, business, art, finance, social sciences, and more. |
Computerbasedmath.org» Join the initiative for modernizing math education. | Online Integral Calculator» Solve sầu integrals with cheap-kenya-vacation-tips.com|Alpha. | Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own. |
cheap-kenya-vacation-tips.com Problem Generator» Unlimited random practice problems & answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. | cheap-kenya-vacation-tips.com Education Portal» Collection of teaching & learning tools built by cheap-kenya-vacation-tips.com education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. | cheap-kenya-vacation-tips.com Language» Knowledge-based programming for everyone. |
![]() | © 1999-2021 cheap-kenya-vacation-tips.com Research, Inc. | Terms of Use |