The disclosed embodiments provide a system that operates a switch fabric. During operation, the system creates a set of virtual links for a first set of physical ports in the switch fabric. Next, the system uses a set of virtual port numbers to create a set of mappings between the set of virtual links and a second set of physical ports in the switch fabric, wherein the second set of physical ports is connected to the first set of physical ports using a single physical link. The system then uses the mappings to provide non-blocking behavior in traffic from the first set of physical ports to the second set of physical ports.