Efficient multi-UAV exploration under limited communication is severely bottlenecked by inadequate task representation and allocation. Previous task representations either impose heavy communication requirements for coordination or lack the flexibility to handle complex environments, often leading to inefficient traversal. Furthermore, short-horizon allocation strategies neglect spatiotemporal contiguity, causing non-contiguous assignments and frequent cross-region detours. To address this, we propose C$^2$-Explorer, a decentralized framework that constructs a connectivity graph to decompose disconnected unknown components into independent task units. We then introduce a contiguity-driven allocation formulation with a graph-based neighborhood penalty to discourage non-adjacent assignments, promoting more contiguous task sequences over time. Extensive simulation experiments show that C$^2$-Explorer consistently outperforms state-of-the-art (SOTA) baselines, reducing average exploration time by 43.1\% and path length by 33.3\%. Real-world flights further demonstrate the system's feasibility. The code will be released at https://github.com/Robotics-STAR-Lab/C2-Explorer