We present integrable lattice equations on a two dimensional square lattice
with coupled vertex and bond variables. In some of the models the vertex
dynamics is independent of the evolution of the bond variables, and one can
write the equations as non-autonomous "Yang-Baxter maps". We also present a
model in which the vertex and bond variables are fully coupled. Integrability
is tested with algebraic entropy as well as multidimensional consistencyComment: 15 pages, remarks added, other minor change
