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Profiles of Separations: in Graphs, Matroids, and Beyond

  • Reinhard Diestel
  • Fabian Hundertmark
  • Sahar Lemanczyk
Article

Abstract

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 combina- torial 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.

Mathematics Subject Classification (2010)

05C05 05C40 05C83 05B35 06A07 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Reinhard Diestel
    • 1
  • Fabian Hundertmark
    • 1
  • Sahar Lemanczyk
    • 1
  1. 1.Mathematisches SeminarUniversität HamburgHamburgGermany

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