Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.11287 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913812563623936 |
|---|---|
| author | Mori, Aki Mori, Kenta Ohsugi, Hidefumi |
| author_facet | Mori, Aki Mori, Kenta Ohsugi, Hidefumi |
| contents | 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 $6^{d/2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11287 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Number of facets of symmetric edge polytopes arising from join graphs Mori, Aki Mori, Kenta Ohsugi, Hidefumi Combinatorics 52B20, 52B12 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 $6^{d/2}$. |
| title | Number of facets of symmetric edge polytopes arising from join graphs |
| topic | Combinatorics 52B20, 52B12 |
| url | https://arxiv.org/abs/2312.11287 |