Generalized quasirandom graphs

Authors:
László Lovász;Vera T. Sós
Affiliations:
Microsoft Research, Redmond, WA, USA;Rényi Institute, Budapest, Hungary
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

Citing 2
Cited 7

Hereditary Extended Properties, Quasi-Random Graphs and Induced Subgraphs

Combinatorics, Probability and Computing
The rank of connection matrices and the dimension of graph algebras

European Journal of Combinatorics

Quasi-randomness Is Determined by the Distribution of Copies of a Fixed Graph in Equicardinal Large Sets

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
Finitely forcible graphons

Journal of Combinatorial Theory Series B
The large deviation principle for the Erdős-Rényi random graph

European Journal of Combinatorics
Quasi-random graphs and graph limits

European Journal of Combinatorics
Testability of minimum balanced multiway cut densities

Discrete Applied Mathematics
Limits of permutation sequences

Journal of Combinatorial Theory Series B
Modularity spectra, eigen-subspaces, and structure of weighted graphs

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We prove that if a sequence of graphs has (asymptotically) the same distribution of small subgraphs as a generalized random graph modeled on a fixed weighted graph H, then these graphs have a structure that is asymptotically the same as the structure of H. Furthermore, it suffices to require this for a finite number of subgraphs, whose number and size is bounded by a function of |V(H)|.