Quasi-random graphs, subgraph counts and graph limits, again

Mathematics > Combinatorics [Submitted on 18 Jun 2026] Title:Quasi-random graphs, subgraph counts and graph limits, again View PDF HTML (experimental)Abstract:We study properties of graphs (or rather graph sequences) saying that some restricted count of subgraphs is approximatively what is expected in a random graph. It has been shown by several authors that many such properties characterize quasi-random graphs, but there are also some exceptions. We continue here the line of investigation in Janson and Sós (2013), and introduce some new versions of these properties, in order to better understand why many of these properties are quasi-random, and to understand the structure of the exceptions that are not. A new feature in the proofs is a simple decomposition of the subspace of symmetric functions in $L^2([0,1]^m)$ into subspaces that are irreducible for the action of measure-preserving transformations of $[0,1]$; this simplifies some arguments and gives structure to others. References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.