Complete Partite subgraphs in dense hypergraphs

Abstract

Abstract For a given r ‐uniform hypergraph ${\cal F}$ we study the largest blow‐up of ${\cal F}$ which can be guaranteed in every large r ‐uniform hypergraph with many copies of ${\cal F}$ . For graphs this problem was addressed by Nikiforov, who proved that every n ‐vertex graph that contains Ω( n ℓ ) copies of the complete graph K ℓ must contain a complete ℓ ‐partite graph with Ω(log n ) vertices in each class. We give another proof of Nikiforov's result, make very small progress towards that problem for hypergraphs, and consider a Ramsey‐type problem related to a conjecture of Erdős and Hajnal.© 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012

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• CiteSeer X (The Pennsylvania State University) - View - PDF
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