Optical Burst and Packet Switching (OBS/OPS) are techniques designed to serve higher-layer packet-based communication protocols by allowing statistical multiplexing. Since OBS and OPS networks provide connectionless transport, they both suffer from contention, which occurs when multiple communications want to use simultaneously the same wavelength in a link. This paper proposes a Routing and Wavelength Assignment (RWA) strategy based on the concept of (rooted) collision-free digraph, which represents all paths assigned by the routing to those communications sharing a wavelength. Using the proposed RWA strategy, the contention problem can be successfully solved by using simple mechanisms based on adding a suitable additional delay to burst/packet transmissions. Here we define and characterize the routing-antipodal networks, in which we can define [n/2] pairs of arc-disjoint collision-free digraphs (with n being the number of nodes) that altogether include all arcs of the network. This implies that, using [n/2] wavelengths, we can achieve connectivity between any pair of nodes under the wavelength-continuity constraint. Solutions with fewer wavelengths are also feasible. In particular, if the routing-antipodal network has a trail that passes through all vertices at least once, one wavelength is enough to ensure connectivity between each pair of nodes. We also show that the line digraph technique provides us with a simple tool for obtaining proper collision-free digraphs. The proposed method works in either a synchronous or an asynchronous transmission environment. Also, the arriving and length burst/packet distributions can be of any type, provided that the maximum theoretical offered load is not exceeded.