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A Survey of Hypergraph Ramsey Problems

In: Discrete Mathematics and Applications

Author

Listed:
  • Dhruv Mubayi

    (University of Illinois)

  • Andrew Suk

    (University of California at San Diego)

Abstract

The classical hypergraph Ramsey number r k(s, n) is the minimum N such that for every red-blue coloring of the k-tuples of {1, …, N}, there are s integers such that every k-tuple among them is red, or n integers such that every k-tuple among them is blue. We survey a variety of problems and results in hypergraph Ramsey theory that have grown out of understanding the quantitative aspects of r k(s, n). Our focus is on recent developments and open problems.

Suggested Citation

  • Dhruv Mubayi & Andrew Suk, 2020. "A Survey of Hypergraph Ramsey Problems," Springer Optimization and Its Applications, in: Andrei M. Raigorodskii & Michael Th. Rassias (ed.), Discrete Mathematics and Applications, pages 405-428, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-55857-4_16
    DOI: 10.1007/978-3-030-55857-4_16
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