A flexible topological representation consisting of a two-layer graph structure built on-board an Unmanned Aerial Vehicle (UAV) by continuously filling the free space of an occupancy map with intersecting spheres is proposed in this letter. Most state-of-the-art planning methods find the shortest paths while keeping the UAV at a pre-defined distance from obstacles. Planning over the proposed structure reaches this pre-defined distance only when necessary, maintaining a safer distance otherwise, while also being orders of magnitude faster than other state-of-the-art methods. Furthermore, we demonstrate how this graph representation can be converted into a lightweight shareable topological-volumetric map of the environment, which enables decentralized multi-robot cooperation. The proposed approach was successfully validated in several kilometers of real subterranean environments, such as caves, devastated industrial buildings, and in the harsh and complex setting of the final event of the DARPA SubT Challenge, which aims to mimic the conditions of real search and rescue missions as closely as possible, and where our approach achieved the 2nd place in the virtual track.