Treetopes and their Graphs
Computational Geometry
2020-08-10 v1 Data Structures and Algorithms
Combinatorics
Abstract
We define treetopes, a generalization of the three-dimensional roofless polyhedra (Halin graphs) to arbitrary dimensions. Like roofless polyhedra, treetopes have a designated base facet such that every face of dimension greater than one intersects the base in more than one point. We prove an equivalent characterization of the 4-treetopes using the concept of clustered planarity from graph drawing, and we use this characterization to recognize the graphs of 4-treetopes in polynomial time. This result provides one of the first classes of 4-polytopes, other than pyramids and stacked polytopes, that can be recognized efficiently from their graphs.
Keywords
Cite
@article{arxiv.1510.03152,
title = {Treetopes and their Graphs},
author = {David Eppstein},
journal= {arXiv preprint arXiv:1510.03152},
year = {2020}
}
Comments
16 pages, 8 figures. To appear at 27th ACM-SIAM Symp. on Discrete Algorithms (SODA 2016)