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- Title
Clique-factors in graphs with sublinear $\boldsymbol\ell$ -independence number.
- Authors
Han, Jie; Hu, Ping; Wang, Guanghui; Yang, Donglei
- Abstract
Given a graph $G$ and an integer $\ell \ge 2$ , we denote by $\alpha _{\ell }(G)$ the maximum size of a $K_{\ell }$ -free subset of vertices in $V(G)$. A recent question of Nenadov and Pehova asks for determining the best possible minimum degree conditions forcing clique-factors in $n$ -vertex graphs $G$ with $\alpha _{\ell }(G) = o(n)$ , which can be seen as a Ramsey–Turán variant of the celebrated Hajnal–Szemerédi theorem. In this paper we find the asymptotical sharp minimum degree threshold for $K_r$ -factors in $n$ -vertex graphs $G$ with $\alpha _\ell (G)=n^{1-o(1)}$ for all $r\ge \ell \ge 2$.
- Subjects
INTEGERS
- Publication
Combinatorics, Probability & Computing, 2023, Vol 32, Issue 4, p665
- ISSN
0963-5483
- Publication type
Article
- DOI
10.1017/S0963548323000081