This paper is about extremely robust and lightweight localisation using LiDAR point clouds based on instance segmentation and graph matching. We model 3D point clouds as fully-connected graphs of semantically identified components where each vertex corresponds to an object instance and encodes its shape. Optimal vertex association across graphs allows for full 6-Degree-of-Freedom (DoF) pose estimation and place recognition by measuring similarity. This representation is very concise, condensing the size of maps by a factor of 25 against the state-of-the-art, requiring only 3kB to represent a 1.4MB laser scan. We verify the efficacy of our system on the SemanticKITTI dataset, where we achieve a new state-of-the-art in place recognition, with an average of 88.4% recall at 100% precision where the next closest competitor follows with 64.9%. We also show accurate metric pose estimation performance - estimating 6-DoF pose with median errors of 10 cm and 0.33 deg.