Supported by NSF DMS 0800070; Heisenberg-Programme of the Deutsche Forschungsgemeinschaft (DFG Grant SCHA 1263/4-1); Emory University Research grant.
Complete Partite subgraphs in dense hypergraphs†
Article first published online: 25 JUN 2012
Copyright © 2012 Wiley Periodicals, Inc.
Random Structures & Algorithms
Special Issue: Proceedings of the Fifteenth International Conference “Random Structures and Algorithms”
Volume 41, Issue 4, pages 557–573, December 2012
How to Cite
Rödl, V. and Schacht, M. (2012), Complete Partite subgraphs in dense hypergraphs. Random Struct. Alg., 41: 557–573. doi: 10.1002/rsa.20441
Part of this work was carried out at the Institute of Advanced Studies in Princeton during the special semester on Arithmetic Combinatorics in Fall 2007 organized by J. Bourgain and V. Vu.
- Issue published online: 24 OCT 2012
- Article first published online: 25 JUN 2012
- Manuscript Accepted: 2 MAR 2012
- Manuscript Received: 8 OCT 2011
- NSF. Grant Number: DMS 0800070
- Heisenberg-Programme of the Deutsche Forschungsgemeinschaft
- DFG. Grant Number: SCHA 1263/4-1
- Emory University Research
- Kövari-Sós-Turán theorem;
- Erdős-Hajnal conjecture;
- partite hypergraphs;
For a given r -uniform hypergraph we study the largest blow-up of which can be guaranteed in every large r -uniform hypergraph with many copies of . For graphs this problem was addressed by Nikiforov, who proved that every n -vertex graph that contains Ω(nℓ) copies of the complete graph Kℓ 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