  Recently, two concepts from optimal transport theory have successfully been
brought to the Gromov--Wasserstein (GW) setting. This introduces a linear
version of the GW distance and multi-marginal GW transport. The former can
reduce the computational complexity when computing all GW distances of a large
set of inputs. The latter allows for a simultaneous matching of more than two
marginals, which can for example be used to compute GW barycenters. The aim of
this paper is to show an approximation result which characterizes the linear
version as a limit of a multi-marginal GW formulation.
