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Date: 11-5-2022
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A path constructed by repeatedly finding a path of positive capacity from a source to a sink and then adding it to the flow (Skiena 1990, p. 237).
An augmenting path for a matching is a path with an odd number of edges , , ..., such that and . The symmetric difference of with yields a matching having one more edge than . Augmenting paths are used in the blossom algorithm and Hungarian maximum matching algorithm for finding graph maximum matchings.
Ford, L. R. and Fulkerson, D. R. Flows in Networks. Princeton, NJ: Princeton University Press, 1962.
Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.
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