Given a team of agents on the nodes of a graph-based network, the exploration problem requires each node to be visited by at least one agent. In the classical distributed setting of static networks, agents do not know the topology of the network; in the more recently investigated setting of dynamic networks, they may have prior knowledge about the graph class (e.g., trees, tori, rings) or other parameters (e.g., number of nodes). Gotoh et al. (2021) are the first to study the exploration problem of arbitrary dynamic networks, under the necessary minimal assumption that any two nodes will be connected by a temporal path infinitely often (temporal connectivity assumption). In this paper, we extend their study of exploration under temporal connectivity by considering dangerous dynamic networks, i.e., containing possibly one or more black holes. Whenever an agent enters a black hole, it will be trapped forever. The safe exploration problem requires a team to explore all the safe nodes, ensuring that at least one agent will never be trapped in a black hole. We first prove that, given the necessary (and sufficient) number of agents, a team of oblivious agents can perpetually explore the safe nodes without any prior knowledge of the network or the team, without agent or node IDs, under semi-synchronous schedulers. Then, we provide an algorithm that enables agents to safely explore the network and terminate. In this case, agents are equipped with unique IDs and persistent memory, and they know the number of safe nodes. Yet, in both cases, we prove that it is impossible for a team of agents on dynamic networks to correctly mark only the ports leading to black holes.

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