In this letter, we describe a novel roadmap construction method in unknown environments, which relies on the extraction of the Hamilton-Jacobi skeleton of the free space. This skeleton is used to construct a graph of free-space bubbles, effectively compressing the skeleton information in a sparse data structure but retaining its topology. The bubbles also enforce safety directly in the roadmap structure. We first demonstrate the relevance of this approach for standard path-planning tasks. We also propose a frontiers-based exploration strategy able to autonomously and safely build a complete 2D map of the environment.