Profiles of separations: in graphs, matroids and beyond
  We show that all the tangles in a finite graph or matroid can be distinguished by a single tree-decomposition that is invariant under the automorphisms of the graph or matroid. This comes as a corollary of a similar decomposition theorem for more general combinatorial structures, which has further applications.   These include a new approach to cluster analysis and image segmentation. As another illustration for the abstract theorem, we show that applying it to edge-tangles yields the Gomory-Hu theorem. 
Reinhard Diestel, Fabian Hundertmark, Sahar Lemanczyk
math.CO