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The main result of this work is that an orthogonal access scheme such as TDMAachieves the all-unicast degrees of freedom (DoF) region of the topologicalinterference management (TIM) problem if and only if the network topology graphis chordal bipartite, i.e., every cycle that can contain a chord, does containa chord. The all-unicast DoF region includes the DoF region for any arbitrarychoice of a unicast message set, so e.g., the results of Maleki and Jafar onthe optimality of orthogonal access for the sum-DoF of one-dimensional convexnetworks are recovered as a special case. The result is also established forthe corresponding topological representation of the index coding problem.

TDMA is Optimal for All-unicast DoF Region of TIM if and only if Topology is Chordal Bipartite