Clique-factors in graphs with sublinear ι-independence number

Given a graph G and an integer l >= 2, we denote by a alpha(l) (G) the maximum size of a Ke--free subset of vertices in V(G). A recent question ofNenadov and Pehova asks for determining the best possible minimum degree conditions forcing clique-factors in n-vertex graphs G with alpha(tau) (G)= o(n), which can be seen as a RamseyTuran variant of the celebrated Hajnal-Szemeredi theorem. In this paper we find the asymptotical sharp minimum degree threshold for Kr-factors in n-vertex graphs G with alpha(l) (G) = n(1-o(1)) for all r >= l >= 2.