[hal-01184359] K_\ell^--factors in graphs

Let K_ℓ^- denote the graph obtained from K_ℓ by deleting one edge. We show that for every γ >0 and every integer ℓ≥4 there exists an integer n_0=n_0(γ ,ℓ) such that every graph G whose order n≥n_0 is divisible by ℓ and whose minimum degree is at least (ℓ^2-3ℓ+1 / ℓ(ℓ-2)+γ )n contains a K_ℓ^--factor, i.e. a collection of disjoint copies of K_ℓ^- which covers all vertices of G. This is best possible up to the error term γ n and yields an approximate solution to a conjecture of Kawarabayashi.

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