  The five-point amplitude for the scattering of two distinct scalars with the
emission of one graviton in the final state is calculated in exact kinematics
for Einstein-Hilbert gravity. The result, which satisfies the Steinmann
relations, is expressed in Sudakov variables, finding that it corresponds to
the sum of two gauge invariant contributions written in terms of a new two
scalar - two graviton effective vertex. A similar calculation is carried out in
Quantum Chromodynamics (QCD) for the scattering of two distinct quarks with one
extra gluon in the final state. The effective vertices which appear in both
cases are then evaluated in the multi-Regge limit reproducing the well-known
result obtained by Lipatov where the Einstein-Hilbert graviton emission vertex
can be written as the product of two QCD gluon emission vertices, up to
corrections to preserve the Steinmann relations.
