  The graded algebra Lambda defined by Pierre Vogel is of general interest in
the theory of finite-type invariants of knots and of 3-manifolds because it
acts on the corresponding spaces of connected graphs subject to relations
called IHX and AS. We examine a subalgebra Lambda_0 that is generated by
certain elements called t and x_n with n >= 3. Two families of relations in
Lambda_0 are derived and it is shown that the dimension of Lambda_0 grows at
most quadratically with respect to degree. Under the assumption that t is not a
zero divisor in Lambda_0, a basis of Lambda_0 and an isomorphism from Lambda_0
to a sub-ring of Z[t,u,v] is given.
