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Erdős–Hajnal Problem for H-Free Hypergraphs

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Abstract

This paper deals with the minimum number \(m_H(r)\) of edges in an H-free hypergraph with the chromatic number more than r. We show how bounds on Ramsey and Turán numbers imply bounds on \(m_H(r)\).

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References

  1. Bohman, T., Frieze, A., Mubayi, D.: Coloring \({H}\)-free hypergraphs. Random Struct. Algorithms 36(1), 11–25 (2010)

    Article  MathSciNet  Google Scholar 

  2. Cherkashin, D.D.: On the Erdös-Hajnal problem for 3-graphs. J. Math. Sci. 255(1), 103–108 (2021)

  3. Cherkashin, D., Petrov, F.: Regular behavior of the maximal hypergraph chromatic number. SIAM J. Discret. Math. 34(2), 1326–1333 (2020)

    Article  MathSciNet  Google Scholar 

  4. Conlon, D., Fox, J., Sudakov, B.: Hypergraph Ramsey numbers. J. Am. Math. Soc. 23(1), 247–266 (2010)

    Article  MathSciNet  Google Scholar 

  5. Fox, J., He, X.: Independent sets in hypergraphs with a forbidden link. Proc. Lond. Math. Soc. 123(4), 384–409 (2021)

    Article  MathSciNet  Google Scholar 

  6. Gyárfás, A., Lehel, J.: Trees in greedy colorings of hypergraphs. Discret. Math. 311(2–3), 208–209 (2011)

    Article  MathSciNet  Google Scholar 

  7. Kostochka, A., Mubayi, D., Rödl, V., Tetali, P.: On the chromatic number of set systems. Random Struct. Algorithms 19(2), 87–98 (2001)

    Article  MathSciNet  Google Scholar 

  8. Kostochka, A., Mubayi, D., Verstraete, J.: Hypergraph Ramsey numbers: triangles versus cliques. J. Comb. Theory Ser. A 120(7), 1491–1507 (2013)

    Article  MathSciNet  Google Scholar 

  9. Pluhár, A.: Greedy colorings of uniform hypergraphs. Random Struct. Algorithms 35(2), 216–221 (2009)

    Article  MathSciNet  Google Scholar 

  10. Raigorodskii, A.M., Cherkashin, D.D.: Extremal problems in hypergraph colourings. Russ. Math. Surv. 75(1), 89–146 (2020)

    Article  MathSciNet  Google Scholar 

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Funding

The work was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics "BASIS"

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev Str., 1113, Sofia, Bulgaria

    Danila Cherkashin

  2. The Euler International Mathematical Institute, St. Petersburg, Russia

    Alexey Gordeev & Georgii Strukov

  3. Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden

    Alexey Gordeev

Authors
  1. Danila Cherkashin
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  2. Alexey Gordeev
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  3. Georgii Strukov
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Corresponding author

Correspondence to Alexey Gordeev.

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Cherkashin, D., Gordeev, A. & Strukov, G. Erdős–Hajnal Problem for H-Free Hypergraphs. Graphs and Combinatorics 40, 10 (2024). https://doi.org/10.1007/s00373-023-02737-6

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  • DOI: https://doi.org/10.1007/s00373-023-02737-6

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