Pulmonary diseases rank prominently among the principal causes of death worldwide. Curing them will require, among other things, a better understanding of the complex 3D tree-shaped structures within the pulmonary system, such as airways, arteries, and veins. Traditional approaches using high-resolution image stacks and standard CNNs on dense voxel grids face challenges in computational efficiency, limited resolution, local context, and inadequate preservation of shape topology. Our method addresses these issues by shifting from dense voxel to sparse point representation, offering better memory efficiency and global context utilization. However, the inherent sparsity in point representation can lead to a loss of crucial connectivity in tree-shaped structures. To mitigate this, we introduce graph learning on skeletonized structures, incorporating differentiable feature fusion for improved topology and long-distance context capture. Furthermore, we employ an implicit function for efficient conversion of sparse representations into dense reconstructions end-to-end. The proposed method not only delivers state-of-the-art performance in labeling accuracy, both overall and at key locations, but also enables efficient inference and the generation of closed surface shapes. Addressing data scarcity in this field, we have also curated a comprehensive dataset to validate our approach. Data and code are available at https://github.com/M3DV/pulmonary-tree-labeling.