  Using the double-copy construction of Yang-Mills-Einstein theories formulated
in our earlier work, we obtain compact presentations for single-trace
Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an
arbitrary number of gluons. These are written as linear combinations of
color-ordered Yang-Mills trees, where the coefficients are given by
color/kinematics-satisfying numerators in a Yang-Mills+\phi^3 theory. The
construction outlined in this paper holds in general dimension and extends
straightforwardly to supergravity theories. For one, two, and three external
gravitons, our expressions give identical or simpler presentations of
amplitudes already constructed through string-theory considerations or the
scattering equations formalism. Our results are based on color/kinematics
duality and gauge invariance, and strongly hint at a recursive structure
underlying the single-trace amplitudes with an arbitrary number of gravitons.
For the single-graviton case, we give amplitudes to any loop order and obtain,
through gauge invariance, new loop-level amplitude relations for Yang-Mills
theory.
