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Encyclopedia of Algorithms pp 504–506Cite as

Maximum Matching

2004; Mucha, Sankowski

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Problem Definition

Let \( { G=(V,E) } \) be an undirected graph, and let \( { n=|V| } \), \( { m=|E| } \). A matching in G is a subset \( { M \subseteq E } \), such that no two edges of M have a common endpoint. A perfect matching is a matching of cardinality \( { n/2 } \). The most basic matching related problems are: finding a maximum matching (i. e. a matching of maximum size) and, as a special case, finding a perfect matching if one exists. One can also consider the case where a weight function \( { w\colon E\rightarrow \mathbb{R} } \) is given and the problem is to find a maximum weight matching.     

The maximum matching and maximum weight matching are two of the most fundamental algorithmic graph problems. They have also played a major role in the development of combinatorial optimization and algorithmics. An excellent account of this can be found in a classic monograph [10] by Lovász and Plummer devoted entirely to matching problems. A more up-to-date, but also more technical...

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, Institute of Informatics, Warsaw, Poland

    Marcin Mucha

Authors
  1. Marcin Mucha
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Mucha, M. (2008). Maximum Matching. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_225

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