The notion of path matching was introduced by Cunningham and Geelen in 1997. Besides the existence of minmax formula and polyhedral results, the problem of presenting an explicit polynomial time combinatorial algorithm for maximum path matching remained open for more than eight years. Recently, Pap has given such algorithm for a slightly more general problem related to so called even factors.
In this talk we shall discuss these problems, Pap's algorithm, and possible generalizations.