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Clique-factors in graphs with sublinear $\boldsymbol\ell$-independence number

Published online by Cambridge University Press:  24 April 2023

Jie Han
School of Mathematics and Statistics and Center for Applied Mathematics, Beijing Institute of Technology, Beijing, China
Ping Hu
School of Mathematics, Sun Yat-sen University, Guangzhou, China
Guanghui Wang
School of Mathematics, Shandong University, Jinan, China
Donglei Yang*
Data Science Institute, Shandong University, Shandong, China
Corresponding author: Donglei Yang; Email:


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 $r\ge \ell \ge 2$ .

MSC classification

© The Author(s), 2023. Published by Cambridge University Press

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