  A simple closed curve in the boundary surface of a handlebody is called
primitive if there exists an essential disk in the handlebody whose boundary
circle intersects the curve transversely in a single point. The primitive curve
complex is then defined to be the full subcomplex of the curve complex for the
boundary surface, spanned by the vertices of primitive curves. Given any two
primitive curves, we construct a sequence of primitive curves from one to the
other one satisfying a certain property. As a consequence, we prove that the
primitive curve complex for the handlebody is connected.
