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Paths, Trees, and Flowers

Published online by Cambridge University Press:  20 November 2018

Jack Edmonds*
Affiliation:
National Bureau of Standards and Princeton University
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A graph G for purposes here is a finite set of elements called vertices and a finite set of elements called edges such that each edge meets exactly two vertices, called the end-points of the edge. An edge is said to join its end-points.

A matching in G is a subset of its edges such that no two meet the same vertex. We describe an efficient algorithm for finding in a given graph a matching of maximum cardinality. This problem was posed and partly solved by C. Berge; see Sections 3.7 and 3.8.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Berge, C., Two theorems in graph theory, Proc. Natl. Acad. Sci. U.S., 43 (1957), 842–4.CrossRefGoogle ScholarPubMed
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3. Edmonds, J., Covers and packings in a family of sets, Bull. Amer. Math. Soc, 68 (1962), 494–9.CrossRefGoogle Scholar
4. Edmonds, J., Maximum matching and a polyhedron with (0, 1) vertices, appearing in J. Res. Natl. Bureau Standards 69B (1965).Google Scholar
5. Ford, L. R. Jr. and Fulkerson, D. R., Flows in networks (Princeton, 1962).Google Scholar
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9. Witzgall, C. and Zahn, C. T. Jr., Modification of Edmonds﹜ algorithm for maximum matching of graphs, appearing in J. Res. Natl. Bureau Standards 69B (1965).Google Scholar
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