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October 2, 2025Open Access

Polynomial-to-exponential transition in 3-uniform Ramsey numbers

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Authors

RARuben AscoliXHXiaoyu HeHYHung-Hsun Hans Yu

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Overview

This research proves the Ramsey number conjecture for 3-uniform hypergraphs, indicating edges grow polynomials or exponentials based on conditions.

Key Points

  • The conjecture for 3-uniform Ramsey numbers is proven, showing a shift from polynomial to exponential growth in relation to parameters.
  • The primary condition involves the balance between red edges and blue cliques, impacting edge formulations in hypergraphs.
  • A novel Turán-type problem was solved involving maximum edges under specific component constraints within hypergraphs.
  • The balanced iterated blowup of an edge serves as the extreme case across varying vertex counts, highlighting its geometric significance.

Cite This Study

Ascoli et al. (2025) studied this question.

synapsesocial.com/papers/68de5da283cbc991d0a208a3https://doi.org/10.48550/arxiv.2507.09434
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