For any graph H there exists C(H) such that every sufficiently large n-vertex graph with d(x)+d(y) ≥ 2(1−1/χ_cr(H))n for every non-edge xy contains an H-tiling covering all but at most C(H) vertices.
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An Ore-type condition for $H$-tilings in graphs
For any graph H there exists C(H) such that every sufficiently large n-vertex graph with d(x)+d(y) ≥ 2(1−1/χ_cr(H))n for every non-edge xy contains an H-tiling covering all but at most C(H) vertices.