Flow polytopes for extensions of bipartite graphs
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918161853448192 |
|---|---|
| author | Braun, Benjamin Bruegge, Kaitlin Davis, Robert Hanely, Derek |
| author_facet | Braun, Benjamin Bruegge, Kaitlin Davis, Robert Hanely, Derek |
| contents | The space of unit flows on a finite acyclic directed graph is a lattice polytope called the flow polytope of the graph. Given a bipartite graph $G$ with minimum degree at least two, we construct two associated acyclic directed graphs: the extension of $G$ and the almost-degree-whiskered graph of $G$. We prove that the normalized volume of the flow polytope for the extension of $G$ is equal to the number of matchings in the almost-degree-whiskered graph of $G$. Further, we refine this result by proving that the Ehrhart $h^*$-polynomial of the flow polytope for the extension of $G$ is equal to the unsigned matching polynomial of the almost-degree-whiskered graph of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flow polytopes for extensions of bipartite graphs Braun, Benjamin Bruegge, Kaitlin Davis, Robert Hanely, Derek Combinatorics The space of unit flows on a finite acyclic directed graph is a lattice polytope called the flow polytope of the graph. Given a bipartite graph $G$ with minimum degree at least two, we construct two associated acyclic directed graphs: the extension of $G$ and the almost-degree-whiskered graph of $G$. We prove that the normalized volume of the flow polytope for the extension of $G$ is equal to the number of matchings in the almost-degree-whiskered graph of $G$. Further, we refine this result by proving that the Ehrhart $h^*$-polynomial of the flow polytope for the extension of $G$ is equal to the unsigned matching polynomial of the almost-degree-whiskered graph of $G$. |
| title | Flow polytopes for extensions of bipartite graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.26445 |