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PreprintCC BY-NC-ND 4.0arXiv

Off-diagonal Ramsey numbers for 3-uniform tight hypergraph cycles

Abstract

Let C(3)n be the $3$-uniform tight cycle on n vertices, that is, the $3$-uniform hypergraph on a cyclically ordered set of n vertices whose edges are precisely the triples of consecutive vertices in the given cyclic order. We asymptotically determine the off-diagonal Ramsey numbers of $3$-uniform tight cycles. This is an off-diagonal analogue of a result of Haxell, Łuczak, Peng, Rödl, Ruciński and Skokan [Combin.\ Probab.\ Comput.\ 18 (2009), no.\ 1-2, 165--203] on the diagonal Ramsey numbers of $3$-uniform tight cycles.

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BibTeX
@misc{hng2026offdiagonal,
  title = {{Off-diagonal Ramsey numbers for 3-uniform tight hypergraph cycles}},
  author = {Eng Keat Hng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39578},
  eprint = {2610.39578},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39578},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Off-diagonal Ramsey numbers for 3-uniform tight hypergraph cycles
AU  - Eng Keat Hng
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39578
UR  - https://arxiv.org/abs/2610.39578
AB  - Let C^(3)_n be the $3$-uniform tight cycle on n vertices, that is, the $3$-uniform hypergraph on a cyclically ordered set of n vertices whose edges are precisely the triples of consecutive vertices in the given cyclic order. We asymptotically determine the off-diagonal Ramsey numbers of $3$-uniform tight cycles. This is an off-diagonal analogue of a result of Haxell, Łuczak, Peng, Rödl, Ruciński and Skokan [Combin.\ Probab.\ Comput.\ 18 (2009), no.\ 1-2, 165--203] on the diagonal Ramsey numbers of $3$-uniform tight cycles.
ER  -