Finite Sholander Trees, Trees, and their Betweenness
Combinatorics
2011-01-18 v1
Abstract
We provide a proof of Sholander's claim (Trees, lattices, order, and betweenness, Proc. Amer. Math. Soc. 3, 369-381 (1952)) concerning the representability of collections of so-called segments by trees, which yields a characterization of the interval function of a tree. Furthermore, we streamline Burigana's characterization (Tree representations of betweenness relations defined by intersection and inclusion, Mathematics and Social Sciences 185, 5-36 (2009)) of tree betweenness and provide a relatively short proof.
Keywords
Cite
@article{arxiv.1101.2957,
title = {Finite Sholander Trees, Trees, and their Betweenness},
author = {Vašek Chvátal and Dieter Rautenbach and Philipp Matthias Schäfer},
journal= {arXiv preprint arXiv:1101.2957},
year = {2011}
}
Comments
8 pages