Triangle-tilings in graphs without large independent sets

We study the minimum degree necessary to guarantee the existence of perfect and almost-perfect triangle-tilings in an n-vertex graph G with sublinear independence number. In this setting, we show that if δ(G)≥n/3+o(n) then G has a triangle-tiling covering all but at most four vertices. Also, for every r≥5, we asymptotically determine the minimum degree threshold for a perfect triangle-tiling under the additional assumptions that G is Kr-free and n is divisible by 3.