  In this note, we provide two characterizations of the set of integer points
in an integral bisubmodular polyhedron. Our characterizations do not require
the assumption that a given set satisfies the hole-freeness, i.e., the set of
integer points in its convex hull coincides with the original set. One is a
natural multiset generalization of the exchange axiom of a delta-matroid, and
the other comes from the notion of the tangent cone of an integral bisubmodular
polyhedron.
