In the context of sixth-generation (6G) networks, emergency management systems based on wireless communications have recently gained increasing interest. Hereby, fundamentals and open problems of post-disaster communications are discussed, especially focusing on their topological aspects. The motivation behind this choice is that whenever a natural or man-made disaster occurs, there is a high chance that the terrestrial communication infrastructure is compromised, and therefore alternative networks need to be deployed efficiently in order to enable the majority of the civilians and first responders to communicate. In this article, we first provide a brief review of existing aerial ad hoc networks for post-disaster communications. Next, we shed light on some new aspects of this problem, which are related to the topology of the network supporting the impacted area. Finally, with the aid of selected simulation results, we show how the cellular infrastructure requirements for a disaster-struck region significantly depend on its location and extension.