Tree sets
Combinatorics
2017-02-28 v3
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.
Keywords
Cite
@article{arxiv.1512.03781,
title = {Tree sets},
author = {Reinhard Diestel},
journal= {arXiv preprint arXiv:1512.03781},
year = {2017}
}