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arXiv · 1807.10203

A degree sequence Koml\'{o}s theorem

Joseph Hyde·Hong Liu·Andrew Treglown
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Abstract

An important result of Koml\'os [Tiling Tur\'an theorems, Combinatorica, 2000] yields the asymptotically exact minimum degree threshold that ensures a graph $G$ contains an $H$-tiling covering an $x$th proportion of the vertices of $G$ (for any fixed $x \in (0,1)$ and graph $H$). We give a degree sequence strengthening of this result which allows for a large proportion of the vertices in the host graph $G$ to have degree substantially smaller than that required by Koml\'os' theorem. We also demonstrate that for certain graphs $H$, the degree sequence condition is essentially best possible in more than one sense.

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Joseph Hyde, Hong Liu, Andrew Treglown. 2018-07-26. A degree sequence Koml\'{o}s theorem. https://arxiv.org/abs/1807.10203

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