Rhombus Criterion and the Chordal Graph Polytope
Combinatorics
2023-05-10 v1
Abstract
The purpose of this paper is twofold. We investigate a simple necessary condition, called the rhombus criterion, for two vertices in a polytope not to form an edge and show that in many examples of -polytopes it is also sufficient. We explain how also when this is not the case, the criterion can give a good algorithm for determining the edges of high-dimenional polytopes. In particular we study the Chordal graph polytope, which arises in the theory of causality and is an important example of a characteristic imset polytope. We prove that, asymptotically, for almost all pairs of vertices the rhombus criterion holds. We conjecture it to hold for all pairs of vertices.
Keywords
Cite
@article{arxiv.2305.05275,
title = {Rhombus Criterion and the Chordal Graph Polytope},
author = {Svante Linusson and Petter Restadh},
journal= {arXiv preprint arXiv:2305.05275},
year = {2023}
}