Abstract
Dedicated to Endre Szemerédi on the occasion of his 70th birthday In this paper we highlight a topological aspect of the graph limit theory. 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.
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© 2010 János Bolyai Mathematical Society and Springer-Verlag
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Lovász, L., Szegedy, B. (2010). Regularity Partitions and The Topology of Graphons. In: Bárány, I., Solymosi, J., Sági, G. (eds) An Irregular Mind. Bolyai Society Mathematical Studies, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14444-8_12
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DOI: https://doi.org/10.1007/978-3-642-14444-8_12
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