  We promote the open-closed string map, originally formulated by Seiberg \&
Witten, to a solution generating prescription in generalized supergravity. The
approach hinges on a knowledge of an antisymmetric bivector $\Theta$, built
from antisymmetric products of Killing vectors, which is specified by the
equations of motion. In the cases we study, the equations of motion reproduce
the Classical Yang-Baxter equation (CYBE) and $\Theta$ is the most general
$r$-matrix solution. Our work generalizes Yang-Baxter deformations to non-coset
spaces and unlocks gravity as a means to classify $r$-matrix solutions to the
CYBE.
