  The perfectly matchable subgraph polytope of a graph is a (0,1)-polytope
associated with the vertex sets of matchings in the graph. In this paper, we
study algebraic properties (compressedness, Gorensteinness) of the toric rings
of perfectly matchable subgraph polytopes. In particular, we give a complete
characterization of a graph whose perfectly matchable subgraph polytope is
compressed.
