The independence and clique cover numbers of the squarefree graph
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913923505061888 |
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| author | Alexeev, Boris Mixon, Dustin G. Sawin, Will |
| author_facet | Alexeev, Boris Mixon, Dustin G. Sawin, Will |
| contents | We determine the largest subset $A\subseteq \{1,\dotsc,n\}$ such that for all $a,b\in A$, the product $ab$ is not squarefree. Specifically, the maximum size is achieved by the complement of the odd squarefree numbers.
This resolves a problem of Paul Erdős and András Sárközy from 1992. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The independence and clique cover numbers of the squarefree graph Alexeev, Boris Mixon, Dustin G. Sawin, Will Combinatorics Number Theory We determine the largest subset $A\subseteq \{1,\dotsc,n\}$ such that for all $a,b\in A$, the product $ab$ is not squarefree. Specifically, the maximum size is achieved by the complement of the odd squarefree numbers. This resolves a problem of Paul Erdős and András Sárközy from 1992. |
| title | The independence and clique cover numbers of the squarefree graph |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2507.01928 |