# $K_{\ell}^{-}$-factors in graphs

Abstract : 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 $(\frac{ℓ^2-3ℓ+1}{/ ℓ(ℓ-2)}+γ )n$ 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 $γn$ and yields an approximate solution to a conjecture of Kawarabayashi.
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Type de document :
Communication dans un congrès
Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.199-202, 2005, DMTCS Proceedings
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https://hal.inria.fr/hal-01184359
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• HAL Id : hal-01184359, version 1

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Daniela Kühn, Deryk Osthus. $K_{\ell}^{-}$-factors in graphs. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.199-202, 2005, DMTCS Proceedings. 〈hal-01184359〉

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