Work

Number of facets of symmetric edge polytopes arising from join graphs

Year: 2025

Type: article

Abstract: Symmetric edge polytopes of graphs are important object in Ehrhart theory, and have an application to Kuramoto models. In the present paper, we study the upper and lower bounds for the number of facets of symmetric edge polytopes of connected graphs conjectured by Braun and Bruegge. In particular, we show that their conjecture is true for any graph that is the join of two graphs (equivalently, for any connected graph whose complement graph is not connected). It is known that any symmetric edge polytope is a centrally symmetric reflexive polytope. Hence our results give a partial answer to Nill’s conjecture: the number of facets of a d -dimensional reflexive polytope is at most 6 d / 2 .

Source: European Journal of Combinatorics

DOI: 10.1016/j.ejc.2025.104165

Authors: Aki Mori, Kenta Mori, Hidefumi Ohsugi

Institution: Kwansei Gakuin University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,560

Funders: Japan Society for the Promotion of Science London, Japan Society for the Promotion of Science