Work

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

Year: 2026

Type: preprint

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 $R(3,k)\le (1+o(1))(k^2/\log k)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.01782

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

Institutions: University of Colorado Denver, University of Denver, University of Johannesburg

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: FRG: Collaborative Research: Extremal Combinatorics and Flag Algebras

OpenAlex ID: W7207808327

Cites: 13

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Related to: 10