On perfect subdivision tilings

For a given graph H , we say that a graph G has a perfect H -subdivision tiling if G contains a collection of vertex-disjoint subdivisions of H covering all vertices of $G.$ Let δ sub(n, H) be the smallest integer k such that any n -vertex graph G with minimum degree at least k has a perfect H -subdivision tiling. For every graph H , we asymptotically determined the value of δ sub(n, H) . More precisely, for every graph H with at least one edge, there is an integer hcfξ(H) and a constant 1 < ξ ^*(H)≤ 2 that can be explicitly determined by structural properties of H such that δ sub(n, H) = (1 - 1/ξ ^*(H) + o(1) )n holds for all n and H unless hcfξ(H) = 2 and n is odd. When hcfξ(H) = 2 and n is odd, then we show that δ sub(n, H) = (1/2 + o(1) )n .