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An important result of Komlós [Tiling Turán 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 Komlós's theorem. We also demonstrate that for certain graphs $H$, the degree sequence condition is essentially best possible in more than one sense.
|Journal||SIAM Journal on Discrete Mathematics|
|Publication status||Published - 22 Oct 2019|
- Degree sequence
- Graph tilings
- Regularity method
ASJC Scopus subject areas
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- 1 Finished
EPSRC Fellowship: Dr Andrew Treglown - Independence in groups, graphs and the integers
Engineering & Physical Science Research Council
1/06/15 → 31/05/18
Project: Research Councils