Hereditary Extended Properties, Quasi-Random Graphs and Induced Subgraphs
Combinatorics, Probability and Computing
Limits of dense graph sequences
Journal of Combinatorial Theory Series B
Generalized quasirandom graphs
Journal of Combinatorial Theory Series B
The effect of induced subgraphs on quasi-randomness
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Quasi-randomness of graph balanced cut properties
Random Structures & Algorithms
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We use the theory of graph limits to study several quasi-random properties, mainly dealing with various versions of hereditary subgraph counts. The main idea is to transfer the properties of (sequences of) graphs to properties of graphons, and to show that the resulting graphon properties only can be satisfied by constant graphons. These quasi-random properties have been studied before by other authors, but our approach gives proofs that we find cleaner, and which avoid the error terms and @e in the traditional arguments using the Szemeredi regularity lemma. On the other hand, other technical problems sometimes arise in analysing the graphon properties; in particular, a measure-theoretic problem on elimination of null sets that arises in this way is treated in an appendix.