  In the gauge-theoretic formulation of gravity the cubic vertex becomes simple
enough for some graviton scattering amplitudes to be computed using
Berends-Giele-type recursion relations. We present such a computation for the
current with all same helicity on-shell gravitons. Once the recursion relation
is set up and low graviton number cases are worked out, a natural guess for the
solution in terms of a sum over trees presents itself readily. The solution can
also be described either in terms of the half-soft function familiar from the
1998 paper by Bern, Dixon, Perelstein and Rozowsky or as a matrix determinant
similar to one used by Hodges for MHV graviton amplitudes. This solution also
immediate suggests the correct guess for the MHV graviton amplitude formula, as
is contained in the already mentioned 1998 paper. We also obtain the recursion
relation for the off-shell current with all but one same helicity gravitons.
