Finitely forcible graphons with an almost arbitrary structure

A basic result from the theory of quasirandom graphs, due to Andrew Thomason, is that if is a graph with vertices and density , and if the number of 4-cycles in is approximately , then resembles a random graph of the same density. In particular, between any two sets and of vertices the number of edg...

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Bibliographic Details
Published in:Discrete analysis 2020
Main Authors: Noel, Jonathan, Kral, Daniel, Lovasz, Laszlo Miklos, Sosnovec, Jakub
Format: Article
Language:English
Online Access:Get full text
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Summary:A basic result from the theory of quasirandom graphs, due to Andrew Thomason, is that if is a graph with vertices and density , and if the number of 4-cycles in is approximately , then resembles a random graph of the same density. In particular, between any two sets and of vertices the number of edges is approximately . (Here, “approximately” means "to within a small fraction of , so the statement is non-trivial only for sets and that are not too small.)
ISSN:2397-3129
2397-3129
DOI:10.19086/da.12058