We study the exploration problem by mobile agents in two prominent models of dynamic graphs: $1$-Interval Connectivity and Connectivity Time. The $1$-Interval Connectivity model was introduced by Kuhn et al.~[STOC 2010], and the Connectivity Time model was proposed by Michail et al.~[JPDC 2014]. Recently, Saxena et al.~[TCS 2025] investigated the exploration problem under both models. In this work, we first strengthen the existing impossibility results for the $1$-Interval Connectivity model. We then show that, in Connectivity Time dynamic graphs, exploration is impossible with $\frac{(n-1)(n-2)}{2}$ mobile agents, even when the agents have full knowledge of all system parameters, global communication, full visibility, and infinite memory. This significantly improves the previously known bound of $n$. Moreover, we prove that to solve exploration with $\frac{(n-1)(n-2)}{2}+1$ agents, $1$-hop visibility is necessary. Finally, we present an exploration algorithm that uses $\frac{(n-1)(n-2)}{2}+1$ agents, assuming global communication, $1$-hop visibility, and $O(\log n)$ memory per agent.

翻译：本文研究移动智能体在两种重要动态图模型中的探索问题：$1$-区间连通性模型与连通时间模型。$1$-区间连通性模型由Kuhn等人~[STOC 2010]提出，连通时间模型由Michail等人~[JPDC 2014]提出。近期，Saxena等人~[TCS 2025]对这两种模型下的探索问题进行了研究。本工作中，我们首先强化了$1$-区间连通性模型下已有的不可能性结果。随后证明在连通时间动态图中，即使智能体完全掌握所有系统参数、具备全局通信能力、全视野可见性与无限内存，使用$\frac{(n-1)(n-2)}{2}$个移动智能体仍无法完成探索任务。该结论显著改进了此前已知的$n$界限制。进一步地，我们证明若采用$\frac{(n-1)(n-2)}{2}+1$个智能体解决探索问题，则$1$-跳视野是必要条件。最后，我们提出一种探索算法，该算法在假设具备全局通信、$1$-跳视野且每个智能体配备$O(\log n)$内存的条件下，使用$\frac{(n-1)(n-2)}{2}+1$个智能体即可完成探索。