Hereditarily extended properties, quasi-random graphs and not necessarily induced subgraphs

Abstract

Recently much attention has been focused on the theory of quasi-random graph and hypergraph properties. The class of quasi-random graphs is defined by certain equivalent graph properties possessed by random graphs. We shall investigate propertiesP which do not imply quasi-randomnes for sequences (G n ) of graphs on their own, but do imply if they hold not only for the whole graphG n but also for every sufficiently large subgraph ofG n . Here the properties are strongly connected to countingnot necessarily induced subgraphs of a given type, while in a subsequent paper we shall investigate the properties connected with counting induced subgraphs.

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Dedicated to the memory of Paul Erdős

Research supported by OTKA N1909.

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Simonovits, M., Sós, V.T. Hereditarily extended properties, quasi-random graphs and not necessarily induced subgraphs. Combinatorica 17, 577–596 (1997). https://doi.org/10.1007/BF01195005

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Mathematics Subject Classification (1991)

  • 05C80