Matching polytopes, Gorensteinness, and the integer decomposition property
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913427670171648 |
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| author | Eisley, Benjamin Matsushita, Koji Vindas-Meléndez, Andrés R. |
| author_facet | Eisley, Benjamin Matsushita, Koji Vindas-Meléndez, Andrés R. |
| contents | The matching polytope of a graph $G$ is the convex hull of the indicator vectors of the matchings on $G$. We characterize the graphs whose associated matching polytopes are Gorenstein, and then prove that all Gorenstein matching polytopes possess the integer decomposition property. As a special case study, we examine the matching polytopes of wheel graphs and show that they are not Gorenstein, but do possess the integer decomposition property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08820 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matching polytopes, Gorensteinness, and the integer decomposition property Eisley, Benjamin Matsushita, Koji Vindas-Meléndez, Andrés R. Combinatorics The matching polytope of a graph $G$ is the convex hull of the indicator vectors of the matchings on $G$. We characterize the graphs whose associated matching polytopes are Gorenstein, and then prove that all Gorenstein matching polytopes possess the integer decomposition property. As a special case study, we examine the matching polytopes of wheel graphs and show that they are not Gorenstein, but do possess the integer decomposition property. |
| title | Matching polytopes, Gorensteinness, and the integer decomposition property |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.08820 |