Netlike partial cubes II. Retracts and netlike subgraphs

First we show that the class of netlike partial cubes is closed under retracts. Then we prove, for a subgraph G of a netlike partial cube H , the equivalence of the assertions: G is a netlike subgraph of H ; G is a hom-retract of H ; G is a retract of H . Finally we show that a non-trivial netlike partial cube G , which is a retract of some bipartite graph H , is also a hom-retract of H if and only if G contains at most one convex cycle of length greater than 4.