Clique-factors in graphs with low $K_{\ell}$-independence number
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911166027005952 |
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| author | Chen, Ming Han, Jie Yang, Donglei |
| author_facet | Chen, Ming Han, Jie Yang, Donglei |
| contents | Given $r\in \mathbb{N}$ with $r\geq 4$, we show that there exists $n_0\in \mathbb{N}$ such that for every $n\geq n_0$, every $n$-vertex graph $G$ with $δ(G)\geq (\frac{1}{2}+o(1))n$ and $α_{r-2}(G)=o(n)$ contains a $K_{r}$-factor. This resolves the first open case of a question proposed by Nenadov and Pehova, and reiterated by Knierm and Su. We further introduce two lower bound constructions that, along with some known results, fully resolve a question presented by Balogh, Molla, and Sharifzadeh. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16851 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Clique-factors in graphs with low $K_{\ell}$-independence number Chen, Ming Han, Jie Yang, Donglei Combinatorics Given $r\in \mathbb{N}$ with $r\geq 4$, we show that there exists $n_0\in \mathbb{N}$ such that for every $n\geq n_0$, every $n$-vertex graph $G$ with $δ(G)\geq (\frac{1}{2}+o(1))n$ and $α_{r-2}(G)=o(n)$ contains a $K_{r}$-factor. This resolves the first open case of a question proposed by Nenadov and Pehova, and reiterated by Knierm and Su. We further introduce two lower bound constructions that, along with some known results, fully resolve a question presented by Balogh, Molla, and Sharifzadeh. |
| title | Clique-factors in graphs with low $K_{\ell}$-independence number |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.16851 |