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arXiv · 2305.05275

Rhombus Criterion and the Chordal Graph Polytope

Svante Linusson·Petter Restadh
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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 $0/1$-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.

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Svante Linusson, Petter Restadh. 2023-05-09. Rhombus Criterion and the Chordal Graph Polytope. https://arxiv.org/abs/2305.05275

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