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Paths, Trees, and Flowers

  • Jack Edmonds (a1)
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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.

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References
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1. Berge, C., Two theorems in graph theory, Proc. Natl. Acad. Sci. U.S., 43 (1957), 842–4.
2. Berge, C., The theory of graphs and its applications (London, 1962).
3. Edmonds, J., Covers and packings in a family of sets, Bull. Amer. Math. Soc, 68 (1962), 494–9.
4. Edmonds, J., Maximum matching and a polyhedron with (0, 1) vertices, appearing in J. Res. Natl. Bureau Standards 69B (1965).
5. Ford, L. R. Jr. and Fulkerson, D. R., Flows in networks (Princeton, 1962).
6. Hoffman, A. J., Some recent applications of the theory of linear inequalities to extremal combinatorial analysis, Proc. Symp. on Appl. Math., 10 (1960), 113–27.
7. Norman, R. Z. and Rabin, M. O., An algorithm for a minimum cover of a graph, Proc. Amer. Math. Soc, 10 (1959), 315–19.
8. Tutte, W. T., The factorization of linear graphs, J. London Math. Soc, 22 (1947), 107–11.
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).
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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