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Abstract
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.
Original language  English 

Pages (fromto)  20412061 
Journal  SIAM Journal on Discrete Mathematics 
Volume  33 
Issue number  4 
DOIs  
Publication status  Published  22 Oct 2019 
Keywords
 Degree sequence
 Graph tilings
 Regularity method
ASJC Scopus subject areas
 General Mathematics
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Dive into the research topics of 'A degree sequence Komlós theorem'. Together they form a unique fingerprint.Projects
 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