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.
