The number of edges of a symmetric edge polytope
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915684683874304 |
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| author | Codenotti, Giulia Riccardi, Roberto Venturello, Lorenzo |
| author_facet | Codenotti, Giulia Riccardi, Roberto Venturello, Lorenzo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16572 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The number of edges of a symmetric edge polytope Codenotti, Giulia Riccardi, Roberto Venturello, Lorenzo Combinatorics 52B20 (Primary), 52C07, 52B05, 52B12, 05E45 (Secondary) 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. |
| title | The number of edges of a symmetric edge polytope |
| topic | Combinatorics 52B20 (Primary), 52C07, 52B05, 52B12, 05E45 (Secondary) |
| url | https://arxiv.org/abs/2512.16572 |