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Published January 2012 | public
Journal Article

Weak quasi-randomness for uniform hypergraphs


We study quasi‐random properties of k‐uniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this property and our work can be viewed as an extension of the well known Chung‐Graham‐Wilson theorem for quasi‐random graphs. Moreover, let K_k be the complete graph on k vertices and M(k) the line graph of the graph of the k‐dimensional hypercube. We will show that the pair of graphs (K_(k),M(k)) has the property that if the number of copies of both K_k and M(k) in another graph G are as expected in the random graph of density d, then G is quasi‐random (in the sense of the Chung‐Graham‐Wilson theorem) with density close to d.

Additional Information

© 2011 Wiley. Issue online 23 November 2011; version of record online 10 November 2011; manuscript accepted 25 November 2010; manuscript received 30 March 2009.

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