Note on the path-matching formula

As a common generalization of matchings and matroidintersections, W.H. Cunningham and J.F. Geelen introduced thenotion of path-matchings. They proved a min-max formula for themaximum value. Here, we exhibit a simplified version of theirmin-max theorem and provide a purely combinatorial proof. ©2002 Wiley Periodicals, Inc. J Graph Theory 41: 110119, 2002András Frank and László Szegõ, arethe members of the Egerváry Research Group (EGRES).