This paper presents a novel decentralized control strategy for a multi-robot system that enables parallel multi-target exploration while ensuring a time-varying connected topology in cluttered 3D environments. Flexible continuous connectivity is guaranteed by building upon a recent connectivity maintenance method, in which limited range, line-of-sight visibility, and collision avoidance are taken into account at the same time. Completeness of the decentralized multi-target exploration algorithm is guaranteed by dynamically assigning the robots with different motion behaviors during the exploration task. One major group is subject to a suitable downscaling of the main traveling force based on the traveling efficiency of the current leader and the direction alignment between traveling and connectivity force. This supports the leader in always reaching its current target and, on a larger time horizon, that the whole team realizes the overall task in finite time. Extensive Monte Carlo simulations with a group of several quadrotor UAVs show the scalability and effectiveness of the proposed method and experiments validate its practicability.