Proves r(s, k) ≥ Ω(k^{s-1} / (log k)^{2s-4}) for fixed s ≥ 3 and k → ∞, nearly matching the Erdős-Szekeres upper bound and improving the Spencer lower bound for s ≥ 5.
Morris, Some recent results in Ramsey theory
9 Pith papers cite this work. Polarity classification is still indexing.
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The threshold for G(n,p) arrow (mH)_2 is n^{-1/max{m2(H),1}} with m approximately n/(2k-alpha), matching the Rodl-Rucinski threshold for most H.
Authors compute new small two-color ordered and cyclic Ramsey numbers for monotone paths, cycles, stars, complete graphs and nested matchings via SAT solving, determine closed forms for several pairs of graph classes, obtain bounds, apply reinforcement learning for lower bounds, and introduce permut
f^{(4)}_{5^{-},6}(N) equals (log log N) to the Theta(1) power, with improved lower bounds r_4(6,n) >= 2^{2^{c sqrt(n)}} and r_k(k+2,n).
Determines the threshold for R(H;s)subseteq R(Q1,...,Qt) where H is random r-graph and Q_i fixed, for many Q including completes, plus characterizes Ramsey equivalence for highly connected tuples.
New iterative proof of Nikiforov's theorem on H-blowups that improves the constant c_H(γ).
Proves existence of r-graphs G with G not arrowing to (K_t1^r ,...,K_tℓ^r) but arrowing to (K_s^r , K_{tℓ-1}^r) where s = R(...) - 1, extending the r=2 case.
SAT-based computation yields exact small reflective and dihedral Ramsey numbers for several ordered graph families, plus closed formulas and conjectures linking them to ordered and cyclic variants.
The exponent in the lower bound for R(ℓ, Cℓ) increases by a positive amount for every fixed C>1, with asymptotic gain Θ(p_C^{-1/2}/log C) as C grows.
citing papers explorer
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Off-diagonal Ramsey numbers
Proves r(s, k) ≥ Ω(k^{s-1} / (log k)^{2s-4}) for fixed s ≥ 3 and k → ∞, nearly matching the Erdős-Szekeres upper bound and improving the Spencer lower bound for s ≥ 5.
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Ramsey properties for tilings in random graphs
The threshold for G(n,p) arrow (mH)_2 is n^{-1/max{m2(H),1}} with m approximately n/(2k-alpha), matching the Rodl-Rucinski threshold for most H.
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Some results on small ordered and cyclic Ramsey numbers
Authors compute new small two-color ordered and cyclic Ramsey numbers for monotone paths, cycles, stars, complete graphs and nested matchings via SAT solving, determine closed forms for several pairs of graph classes, obtain bounds, apply reinforcement learning for lower bounds, and introduce permut
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A Note on Generalized Erd\H{o}s-Rogers Problems
f^{(4)}_{5^{-},6}(N) equals (log log N) to the Theta(1) power, with improved lower bounds r_4(6,n) >= 2^{2^{c sqrt(n)}} and r_k(k+2,n).
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On the Ramsey classes of random hypergraphs
Determines the threshold for R(H;s)subseteq R(Q1,...,Qt) where H is random r-graph and Q_i fixed, for many Q including completes, plus characterizes Ramsey equivalence for highly connected tuples.
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Finding blowups one vertex at a time
New iterative proof of Nikiforov's theorem on H-blowups that improves the constant c_H(γ).
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A note on hypergraphs with asymmetric Ramsey properties
Proves existence of r-graphs G with G not arrowing to (K_t1^r ,...,K_tℓ^r) but arrowing to (K_s^r , K_{tℓ-1}^r) where s = R(...) - 1, extending the r=2 case.
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Computation of small reflective and dihedral Ramsey numbers
SAT-based computation yields exact small reflective and dihedral Ramsey numbers for several ordered graph families, plus closed formulas and conjectures linking them to ordered and cyclic variants.
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Sharper Ramsey lower bounds from refined Gaussian estimates
The exponent in the lower bound for R(ℓ, Cℓ) increases by a positive amount for every fixed C>1, with asymptotic gain Θ(p_C^{-1/2}/log C) as C grows.