  A maximum stable set in a graph G is a stable set of maximum size. S is a
local maximum stable set if it is a maximum stable set of the subgraph of G
spanned by the union of S and N(S), where N(S) is the neighborhood of S. A
matching M is uniquely restricted if its saturated vertices induce a subgraph
which has a unique perfect matching, namely M itself. One theorem of Nemhauser
and Trotter Jr., working as a useful sufficient local optimality condition for
the weighted maximum stable set problem, ensures that any local maximum stable
set of G can be enlarged to a maximum stable set of G. In one of our previous
papers it is proven that the family of all local maximum stable sets of a
forest forms a greedoid on its vertex set. In this paper we obtain a
generalization of this assertion claiming that the family of all local maximum
stable sets of a bipartite graph G is a greedoid if and only if all maximum
matchings of G are uniquely restricted.
