An Asymptotically Sharp Bound on the Maximum Number of Independent Transversals
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929229386481664 |
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| author | Ruotolo, Jake Wang, Kevin Wei, Fan |
| author_facet | Ruotolo, Jake Wang, Kevin Wei, Fan |
| contents | Let $G$ be a multipartite graph with partition $V_1, V_2,\ldots, V_k$ of $V(G)$. Let $d_{i,j}$ denote the edge density of the pair $(V_i, V_j)$. An independent transversal is an independent set of $G$ with exactly one vertex in each $V_i$. In this paper, we prove an asymptotically sharp upper bound on the maximum number of independent transversals given the $d_{i,j}$'s. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06722 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An Asymptotically Sharp Bound on the Maximum Number of Independent Transversals Ruotolo, Jake Wang, Kevin Wei, Fan Combinatorics 05C35, 05C69 Let $G$ be a multipartite graph with partition $V_1, V_2,\ldots, V_k$ of $V(G)$. Let $d_{i,j}$ denote the edge density of the pair $(V_i, V_j)$. An independent transversal is an independent set of $G$ with exactly one vertex in each $V_i$. In this paper, we prove an asymptotically sharp upper bound on the maximum number of independent transversals given the $d_{i,j}$'s. |
| title | An Asymptotically Sharp Bound on the Maximum Number of Independent Transversals |
| topic | Combinatorics 05C35, 05C69 |
| url | https://arxiv.org/abs/2211.06722 |