H-factors in graphs with small independence number

Let H be an h-vertex graph. The vertex arboricity ar(H) of H is the least integer r such that V(H) can be partitioned into r parts and each part induces a forest in H. We show that for sufficiently large n∈hN, every n-vertex graph G with δ(G)≥max⁡{(1−2f(H)+o(1))n,(12+o(1))n} and α(G)=o(n) contains an H-factor, where f(H)=2ar(H) or 2ar(H)−1. The result can be viewed an analogue of the Alon–Yuster theorem [1] in Ramsey–Turán theory, which generalizes the results of Balogh–Molla–Sharifzadeh [2] and Knierim–Su [21] on clique factors. In particular the degree conditions are asymptotically sharp for infinitely many graphs H which are not cliques.