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.