Abstract—A great deal of work has been done recently on developing techniques for proving deadlock freedom for wormhole routing algorithms. One approach has been to restrict the class of routing algorithms for which the proof technique applies. The other approach is to provide a generic method that can be applied to all routing algorithms. Although this latter approach offers clear advantages, a general technique must deal with many complications. Foremost among these is the issue of irreducible cyclic dependencies that cannot result in deadlock. Such dependencies have been referred to alternatively as unreachable configurations and false resource cycles. In this paper, we apply the notion of unreachable cyclic configurations to oblivious routing algorithms. An oblivious routing algorithm is thus constructed that is deadlock-free, even though there are cycles in the channel dependency graph. The idea of unreachable configurations is then further developed to show various restrictions on when such configurations can exist with oblivious routing algorithms. Finally, the example is generalized to allow the construction of larger networks with unreachable cycles. One benefit of characterizing when unreachable cyclic configurations can occur is that proving deadlock freedom is simplified for networks in which unreachable cycles cannot exist. Another contribution of this work is a first step toward a more formal model of unreachable cycles in wormhole-routed networks.