The p-median polytope of Y-free graphs: An application of the matching theory

Recently, Baiou and Barahona [M. Baiou, F. Barahona, On the p-median polytope of Y-free graphs. Discrete Optimization (in press, available online October 2007)] gave a characterization of the p-median polytope for Y-free graphs. In this paper, we give an alternative proof of this result by reducing the p-median problem in those graphs to a matching problem and then by building upon powerful results from the matching theory.