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arXiv · 2609.01782

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

Samuel Harris·Zion Hefty·Paul Horn·Dylan King·Florian Pfender
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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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Samuel Harris, Zion Hefty, Paul Horn, Dylan King, Florian Pfender. 2026-09-01. A short proof that $R(3,k)=Θ(k^2/\log k)$. https://arxiv.org/abs/2609.01782

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