The number of edges of a symmetric edge polytope

Summary · qwen2.5:32b

The article establishes a sharp lower bound for the number of edges of a symmetric edge polytope based on elementary graph invariants and characterizes graphs that meet this bound; it also explores how the h*-polynomial of these polytopes behaves under edge deletion, connecting to a conjecture by Ohsugi and Tsuchiya.

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Considering the article discusses the symmetric edge polytope of a simple graph and the number of edges in relation to mathematical invariants, it could be interesting to share insights about this mathematical topic and its applications in geometry or graph theory.

Excerpt

arXiv:2512.16572v2 Announce Type: replace 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.