A short proof that $R(3,k)=Θ(k^2/\log k)$

Samuel Harris, Zion Hefty, Paul Horn, Dylan King, Florian Pfender

Source record

Source: arXiv

Published: Sep 1, 2026

arXiv: 2609.01782

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Source abstract

We give a nibble-free construction proving $R(3,k)\ge(1/200+o(1))k^2/\log k$ . We also include Shearer's proof bounding the independence number of a triangle-free graph, which implies $R(3,k)\le (1+o(1))(k^2/\log k)$ .

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