Structural theory of trees. I. Branching and condensations of trees
Combinatorics
2023-01-18 v1 Logic
Abstract
Trees are partial orders in which every element has a linearly ordered set of predecessors. Here we initiate the exploration of the structural theory of trees with the study of different notions of \emph{branching in trees} and of \emph{condensed trees}, which are trees in which every node is a branching node. We then introduce and investigate two different constructions of \emph{tree condensations} -- one shrinking, and the other expanding, the tree to a condensed tree.
Cite
@article{arxiv.2301.06344,
title = {Structural theory of trees. I. Branching and condensations of trees},
author = {Valentin Goranko and Ruaan Kellerman and Alberto Zanardo},
journal= {arXiv preprint arXiv:2301.06344},
year = {2023}
}
Comments
20 pages. To appear in: Contributions to Discrete Mathematics