Mathematics – Combinatorics
Scientific paper
2010-02-23
Mathematics
Combinatorics
25 pages
Scientific paper
We highlight a topological aspect of the graph limit theory. Graphons are limit objects for convergent sequences of dense graphs. We introduce the representation of a graphon on a unique metric space and we relate the dimension of this metric space to the size of regularity partitions. We prove that if a graphon has an excluded induced sub-bigraph then the underlying metric space is compact and has finite packing dimension. It implies in particular that such graphons have regularity partitions of polynomial size.
Lovasz Laszlo
Szegedy Balazs
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