  Relay synchronization in complex networks is characterized by the
synchronization of remote parts of the network due to their interaction via a
relay. In multilayer networks, distant layers that are not connected directly
can synchronize due to signal propagation via relay layers. In this work, we
investigate relay synchronization of partial synchronization patterns like
chimera states in three-layer networks of interacting FitzHugh-Nagumo
oscillators. We demonstrate that the phenomenon of relay synchronization is
robust to topological random inhomogeneities of small-world type in the layer
networks. We show that including randomness in the connectivity structure
either of the remote network layers, or of the relay layer, increases the range
of interlayer coupling strength where relay synchronization can be observed.
