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Separations of Sets

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Abstract

Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as separation systems of graphs, sets, or set bipartitions.

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References

  1. Diestel, R.: Abstract separation systems. Order 35, 157–170 (2018)

    Article  MathSciNet  Google Scholar 

  2. Diestel, R.: Tree sets. Order 35, 171–192 (2018)

    Article  MathSciNet  Google Scholar 

  3. Diestel, R., Hundertmark, F., Lemanczyk, S.: Profiles of separations: in graphs, matroids, and beyond. Combinatorica 39(1), 37–75 (2019)

    Article  MathSciNet  Google Scholar 

  4. Diestel, R., Oum, S.: Tangle-tree duality in abstract separation systems. Submitted, arXiv:1701.02509 (2017)

  5. Diestel, R., Whittle, G.: Tangles and the Mona Lisa. arXiv:1603.06652

  6. Robertson, N., Seymour, P.: Graph minors. X. Obstructions to tree-decomposition. J. Combin. Theory (Series B) 52, 153–190 (1991)

    Article  MathSciNet  Google Scholar 

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Correspondence to Jakob Kneip.

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Bowler, N., Kneip, J. Separations of Sets. Order 37, 411–425 (2020). https://doi.org/10.1007/s11083-019-09512-4

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  • DOI: https://doi.org/10.1007/s11083-019-09512-4

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