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Tree sets

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arxiv 1512.03781 v3 pith:GAULMVEM submitted 2015-12-11 math.CO

Reinhard Diestel This is my paper · ORCID
classification math.CO
keywords treetreesgraphsordersetsmatroidsstructurestructures
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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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  1. On vertex sets inducing tangles

    math.CO 2024-11 conditional novelty 7.0 of 10

    Every k-tangle in a graph is the lift of a k-tangle in a topological minor of size bounded by a function of k, reducing the vertex-set induction problem to bounded-size graphs.

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