TL;DR
This paper investigates infinite tree sets, a generalization of tree-like structures in combinatorics, and characterizes their properties in relation to finite tree sets.
Contribution
It provides a combinatorial characterization of infinite tree sets and explores their relationship with finite tree sets, extending the theory of abstract separation systems.
Findings
Infinite tree sets are characterized combinatorially.
Infinite tree sets relate systematically to finite tree sets.
The study extends the understanding of abstract separation systems.
Abstract
Tree sets are posets with additional structure that generalize tree-like objects in graphs, matroids, or other combinatorial structures. They are a special class of abstract separation systems. We study infinite tree sets and how they relate to the finite tree sets they induce, and obtain a characterization of infinite tree sets in combinatorial terms.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Graph Labeling and Dimension Problems