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Tree Sets

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Abstract

We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and matroids etc.

Unlike graph-theoretical or order trees, these tree sets can provide a suitable formalization of tree structure also for infinite graphs, matroids, and set partitions. Order trees reappear as oriented tree sets.

We show how each of the above structures defines a tree set, and which additional information, if any, is needed to reconstruct it from this tree set.

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Authors and Affiliations

  1. Hamburg University, Hamburg, Germany

    Reinhard Diestel

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  1. Reinhard Diestel
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Diestel, R. Tree Sets. Order 35, 171–192 (2018). https://doi.org/10.1007/s11083-017-9425-4

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  • DOI: https://doi.org/10.1007/s11083-017-9425-4

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