Combinatorica

, Volume 20, Issue 1, pp 61–70 | Cite as

An Algebraic Matching Algorithm

  • James F. Geelen
Original Paper

V

by V skew-symmetric matrix \(\), called the Tutte matrix, associated with a simple graph G=(V,E). He associates an indeterminate \(\) with each \(\), then defines \(\) when \(\), and \(\) otherwise. The rank of the Tutte matrix is exactly twice the size of a maximum matching of G. Using linear algebra and ideas from the Gallai–Edmonds decomposition, we describe a very simple yet efficient algorithm that replaces the indeterminates with constants without losing rank. Hence, by computing the rank of the resulting matrix, we can efficiently compute the size of a maximum matching of a graph.

AMS Subject Classification (1991) Classes:  05C70 

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Copyright information

© János Bolyai Mathematical Society, 2000

Authors and Affiliations

  • James F. Geelen
    • 1
  1. 1.Department of Combinatorics and Optimization, University of Waterloo; Waterloo, Ontario, Canada, N2L 3G1; E-mail: jfgeelen@math.uwaterloo.caCA

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