  A graph embedded in the 3-sphere is called irreducible if it is
non-splittable and for any 2-sphere embedded in the 3-sphere that intersects
the graph at one point the graph is contained in one of the 3-balls bounded by
the 2-sphere. We show that irreducibility is preserved under certain
deformations of embedded graphs. We show that certain embedded graphs are
irreducible.
