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Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs

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Arkiv för Matematik

Abstract

General upper tail estimates are given for counting edges in a random induced subhypergraph of a fixed hypergraph ℋ, with an easy proof by estimating the moments. As an application we consider the numbers of arithmetic progressions and Schur triples in random subsets of integers. In the second part of the paper we return to the subgraph counts in random graphs and provide upper tail estimates in the rooted case.

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References

  1. Dudek, A., Polcyn, J. and Ruciński, A., Subhypergraph counts in extremal and random hypergraphs and the fractional q-independence, J. Comb. Optim.19 (2010), 184–199.

    Article  MathSciNet  MATH  Google Scholar 

  2. Graham, R., Rödl, V. and Ruciński, A., On Schur properties of random subsets of integers, J. Number Theory61 (1996), 388–408.

    Article  MathSciNet  MATH  Google Scholar 

  3. Janson, S., Oleszkiewicz, K. and Ruciński, A., Upper tails for subgraph counts in random graphs, Israel J. Math.142 (2004), 61–92.

    Article  MathSciNet  MATH  Google Scholar 

  4. Janson, S., Łuczak, T. and Ruciński, A., Random Graphs, Wiley, New York, 2000.

    MATH  Google Scholar 

  5. Janson, S. and Ruciński, A., The infamous upper tail, Random Structures Algorithms20 (2002), 317–342.

    Article  MathSciNet  MATH  Google Scholar 

  6. Janson, S. and Ruciński, A., The deletion method for upper tail estimates, Combinatorica24 (2004), 615–640.

    Article  MathSciNet  MATH  Google Scholar 

  7. Łuczak, T. and Prałat, P., Chasing robbers on random graphs: zigzag theorem, Preprint, 2008.

  8. Rödl, V. and Ruciński, A., Rado partition theorem for random subsets of integers, Proc. Lond. Math. Soc.74 (1997), 481–502.

    Article  MATH  Google Scholar 

  9. Vu, V. H., A large deviation result on the number of small subgraphs of a random graph, Combin. Probab. Comput.10 (2001), 79–94.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Uppsala University, P.O. Box 480, SE-751 06, Uppsala, Sweden

    Svante Janson

  2. Department of Discrete Mathematics, Adam Mickiewicz University, ul. Umultowska 87, PL-61-614, Poznań, Poland

    Andrzej Ruciński

Authors
  1. Svante Janson
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  2. Andrzej Ruciński
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Corresponding author

Correspondence to Svante Janson.

Additional information

A. Ruciński supported by Polish grant N201036 32/2546. Research was performed while the authors visited Institut Mittag-Leffler in Djursholm, Sweden, during the program Discrete Probability, 2009.

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Janson, S., Ruciński, A. Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs. Ark Mat 49, 79–96 (2011). https://doi.org/10.1007/s11512-009-0117-1

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  • DOI: https://doi.org/10.1007/s11512-009-0117-1

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