
TL;DR
This paper introduces the concept of tree sets, an abstract framework capturing the core structure of various tree-like combinatorial objects, including infinite graphs and matroids, unifying their formalization.
Contribution
It formalizes tree sets as a unifying abstraction for diverse tree structures, extending applicability to infinite and more complex combinatorial objects.
Findings
Tree sets encompass various tree-like structures in combinatorics.
Order trees are represented as oriented tree sets.
The paper details how different structures can be reconstructed from tree sets.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsConstraint Satisfaction and Optimization · Data Mining Algorithms and Applications
