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This analysis explores conditions leading to polynomial growth of Ramsey numbers in hypergraphs, indicating key structural properties.
A natural open problem in Ramsey theory is to determine those 3 3 -graphs H H for which the off-diagonal Ramsey number r ( H , K n ( 3 ) ) r(H, K_n⁽³⁾) grows polynomially with n n . We make substantial progress on this question by showing that if H H is tightly connected or has at most two tight components, then r ( H , K n ( 3 ) ) r(H, K_n⁽³⁾) grows polynomially if and only if H H is contained in an iterated blowup of an edge.
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Conlon et al. (2025) studied this question.
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