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Published November 2025 | Version Published
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When are off-diagonal hypergraph Ramsey numbers polynomial?

Creators

  • 1. ROR icon California Institute of Technology
  • 2. ROR icon Stanford University
  • 3. ROR icon Rutgers, The State University of New Jersey
  • 4. ROR icon Georgia Institute of Technology
  • 5. ROR icon University of Illinois at Chicago
  • 6. ROR icon University of California, San Diego
  • 7. ROR icon Princeton University

Abstract

A natural open problem in Ramsey theory is to determine those 3-graphs H for which the off-diagonal Ramsey number r(H, Kn(3)) grows polynomially with n. We make substantial progress on this question by showing that if H is tightly connected or has at most two tight components, then r(H,Kn(3))  grows polynomially if and only if H is contained in an iterated blowup of an edge.

Copyright and License

© 2025 American Mathematical Society.

Acknowledgement

We are grateful to Jiaxi Nie, Maya Sankar and Yuval Wigderson for stimulating conversations. We are also grateful to the anonymous reviewers for several helpful remarks.

Funding

The first author was supported by NSF Awards DMS-2054452 and DMS-2348859.
The second author was supported by NSF Award DMS-2154129.
The fourth author was supported by NSF Award DMS-2103154.
The fifth author was supported by NSF Awards DMS-1763317, DMS-1952767 and DMS2153576, by a Humboldt Research Award and by a Simons Fellowship.
The sixth author was supported by an NSF CAREER Award and by NSF Awards DMS1952786 and DMS-2246847.
The seventh author was supported by NSF Award DMS-1800332.

Additional details

Related works

Is new version of
Discussion Paper: arXiv:2411.13812 (arXiv)

Funding

National Science Foundation
DMS-2054452
National Science Foundation
DMS-2348859
National Science Foundation
DMS-2154129
National Science Foundation
DMS-2103154
National Science Foundation
DMS-1763317
National Science Foundation
DMS-1952767
National Science Foundation
DMS-2153576
Alexander von Humboldt Foundation
Simons Foundation
National Science Foundation
DMS-1952786
National Science Foundation
DMS-2246847
National Science Foundation
DMS-1800332

Dates

Submitted
2024-12-14
Available
2025-09-19
Published online

Caltech Custom Metadata

Caltech groups
Division of Physics, Mathematics and Astronomy (PMA) , Mathematics Department
Publication Status
Published