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- Title
A note on pseudorandom Ramsey graphs.
- Authors
Mubayi, Dhruv; Verstraëte, Jacques
- Abstract
For fixed s≥3, we prove that if optimal Ks-free pseudorandom graphs exist, then the Ramsey number r(s,t) is t s−1+o(1) as t→∞. Our method also improves the best lower bounds for r(Cℓ ,t) obtained by Bohman and Keevash from the random Cℓ-free process by polylogarithmic factors for all odd ℓ≥5 and ℓ∈{6,10}. For ℓ=4 it matches their lower bound from the C4-free process. We also prove, via a different approach, that r(C5,t)>(1+o(1))t 11/8 and r(C7 ,t)>(1+o(1))t 11/9 . These improve the exponent of t in the previous best results and appear to be the first examples of graphs F with cycles for which such an improvement of the exponent for r(F,t) is shown over the bounds given by the random F-free process and random graphs.
- Subjects
RAMSEY numbers; RANDOM graphs; FINITE geometries; MATHEMATICAL models; MATHEMATICAL formulas
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2024, Vol 26, Issue 1, p153
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1359