Deformation cones of graphical zonotopes for $K_4$-free graph
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915570241241088 |
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| author | Poullot, Germain |
| author_facet | Poullot, Germain |
| contents | In this paper, we compute a triangulation of certain faces of the submodular cone. More precisely, graphical zonotopes are generalized permutahedra, and hence their deformation cones are faces of the submodular cone. We give a triangulation of these faces for graphs without induced complete sub-graph on 4 vertices. We deduce the rays of these faces: Minkowski indecomposable deformations of these graphical zonotopes are segments and triangles.
Besides, computer experiments lead to examples of graphs without induced complete sub-graph on 5 vertices, whose graphical zonotopes have high dimensional Minkowski indecomposable deformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02669 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformation cones of graphical zonotopes for $K_4$-free graph Poullot, Germain Combinatorics 52B05, 52B11, 52B12, 05C20 In this paper, we compute a triangulation of certain faces of the submodular cone. More precisely, graphical zonotopes are generalized permutahedra, and hence their deformation cones are faces of the submodular cone. We give a triangulation of these faces for graphs without induced complete sub-graph on 4 vertices. We deduce the rays of these faces: Minkowski indecomposable deformations of these graphical zonotopes are segments and triangles. Besides, computer experiments lead to examples of graphs without induced complete sub-graph on 5 vertices, whose graphical zonotopes have high dimensional Minkowski indecomposable deformations. |
| title | Deformation cones of graphical zonotopes for $K_4$-free graph |
| topic | Combinatorics 52B05, 52B11, 52B12, 05C20 |
| url | https://arxiv.org/abs/2404.02669 |