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Regular Partitions of Hypergraphs: Counting Lemmas

Published online by Cambridge University Press:  01 November 2007

VOJTĚCH RÖDL  and
MATHIAS SCHACHT
VOJTĚCH RÖDL
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA (e-mail: rodl@mathcs.emory.edu)
MATHIAS SCHACHT
Affiliation:
Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany (e-mail: schacht@informatik.hu-berlin.de)
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Abstract

We continue the study of regular partitions of hypergraphs. In particular, we obtain corresponding counting lemmas for the regularity lemmas for hypergraphs from our paper ‘Regular Partitions of Hypergraphs: Regularity Lemmas’ (in this issue).

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 6 , November 2007 , pp. 887 - 901
Copyright
Copyright © Cambridge University Press 2007

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References

[1]Avart, C., Rödl, V. and Schacht, M.Every monotone 3-graph property is testable. SIAM J. Discrete Math. 21 (1)73–92.CrossRefGoogle Scholar
[2]Cooley, O., Fountoulakis, N., Kühn, D. and Osthus, D. Embeddings and Ramsey numbers of sparse k-uniform hypergraphs. Submitted.Google Scholar
[3]Erdős, P., Frankl, P. and Rödl, V. (1986) The asymptotic number of graphs not containing a fixed subgraph and a problem for hypergraphs having no exponent. Graphs Combin. 2 113–121.CrossRefGoogle Scholar
[4]Frankl, P. and Rödl, V. (2002) Extremal problems on set systems. Random Struct. Alg. 20 131–164.CrossRefGoogle Scholar
[5]Gowers, W. T. Hypergraph regularity and the multidimensional Szemerédi theorem. Submitted.Google Scholar
[6]Kohayakawa, Y., Rödl, V. and Skokan, J. (2002) Hypergraphs, quasi-randomness, and conditions for regularity. J. Combin. Theory Ser. A 97 307–352.CrossRefGoogle Scholar
[7]Komlós, J., Shokoufandeh, A., Simonovits, M. and Szemerédi, E. (2002) The regularity lemma and its applications in graph theory. In Theoretical Aspects of Computer Science: Tehran 2000, Vol. 2292 of Lecture Notes in Computer Science, Springer, Berlin, pp. 84–112.CrossRefGoogle Scholar
[8]Nagle, B., Rödl, V. and Schacht, M. (2006) The counting lemma for regular k-uniform hypergraphs. Random Struct. Alg. 28 113–179.CrossRefGoogle Scholar
[9]Nagle, B., Rödl, V. and Schacht, M. (2006) Extremal hypergraph problems and the regularity method. In Topics in Discrete Mathematics, Vol. 26 of Algorithms Combin., Springer, Berlin, pp. 247–278.CrossRefGoogle Scholar
[10]Nagle, B., Sayaka, O., Rödl, V. and Schacht, M. On the Ramsey number of sparse 3-graphs. Submitted.Google Scholar
[11]Rödl, V. and Schacht, M. (2007) Regular partitions of hypergraphs: regularity lemmas. Combin. Probab. Comput. 16 (6): 833–885.CrossRefGoogle Scholar
[12]Rödl, V., Schacht, M., Siggers, M. and Tokushige, N. (2007) Integer and fractional packings of hypergraphs. J. Combin. Theory Ser. B 97 245–268.CrossRefGoogle Scholar
[13]Rödl, V. and Skokan, J. (2004) Regularity lemma for k-uniform hypergraphs. Random Struct. Alg. 25 1–42.CrossRefGoogle Scholar
[14]Rödl, V. and Skokan, J. (2006) Applications of the regularity lemma for uniform hypergraphs. Random Struct. Alg. 28 180–194.CrossRefGoogle Scholar
[15]Tao, T. (2006) A variant of the hypergraph removal lemma. J. Combin. Theory Ser. A 113 1257–1280.CrossRefGoogle Scholar