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arXiv · 2512.16572

The number of edges of a symmetric edge polytope

Giulia Codenotti·Roberto Riccardi·Lorenzo Venturello
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Abstract

The symmetric edge polytope of a simple graph is a lattice polytope defined as the convex hull of a subset of the type A roots corresponding to the edges of the graph. In this article we prove a sharp lower bound for the number of edges of the symmetric edge polytope of a graph as a function of elementary graph invariants. Moreover, we characterize graphs attaining this bound. We highlight a connection with the h*-polynomial of such polytopes and, motivated by a conjecture of Ohsugi and Tsuchiya, we investigate the behaviour of such polynomial under edge-deletion in the graph.

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Giulia Codenotti, Roberto Riccardi, Lorenzo Venturello. 2025-12-18. The number of edges of a symmetric edge polytope. https://arxiv.org/abs/2512.16572

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