A General Lower Bound for Collaborative Tree Exploration

We consider collaborative graph exploration with a set of k agents. All agents start at a common vertex of an initially unknown graph with n vertices and need to collectively visit all other vertices. We assume agents are deterministic, moves are simultaneous, and we allow agents to communicate globally. For this setting, we give the first non-trivial lower bounds that bridge the gap between small (\(k \le \sqrt{n}\)) and large (\(k \ge n\)) teams of agents. Remarkably, our bounds tightly connect to existing results in both domains.