, Volume 35, Issue 1, pp 157–170 | Cite as

Abstract Separation Systems

  • Reinhard Diestel


Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree structure theorems in graphs, matroids or CW-complexes to, potentially, image segmentation and cluster analysis. This paper is intended as a concise common reference for the basic definitions and facts about abstract separation systems in these and any future papers using this framework.


Connectivity Graph Tangle Lattice Partial order Tree 


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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Reinhard Diestel
    • 1
  1. 1.Hamburg UniversityHamburgGermany

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