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Quasi-random graphs and graph limits
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2011 (English)In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 32, no 7, 1054-1083 p.Article in journal (Refereed) Published
Abstract [en]

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, measure-theoretic problem on elimination of null sets that arises in this way is treated in an appendix.

Place, publisher, year, edition, pages
2011. Vol. 32, no 7, 1054-1083 p.
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URN: urn:nbn:se:uu:diva-159222DOI: 10.1016/j.ejc.2011.03.011ISI: 000294580100008OAI: oai:DiVA.org:uu-159222DiVA: diva2:444059
Available from: 2011-09-27 Created: 2011-09-26 Last updated: 2012-02-16Bibliographically approved

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