Author

Raphael Steiner

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Preprint Aug 2026

Multicolor Ramsey numbers of odd cycles are superexponential

In a recent breakthrough, OpenAI proved that the $k$-color Ramsey number of the triangle $C_3$ grows super-exponentially, more precisely, they proved that $R_k(C_3)\ge k^{k/3-o(k)}$. In this short note, we present a modification of their recursive construction that works for multicolor Ramsey numbers of fixed odd cycle...

Raphael Steiner · 1 citation

Preprint Aug 2026

Locally bipartite subgraphs via multicolor Ramsey numbers

A famous conjecture of Erd\H{o}s and Hajnal (1969) states that for every integer $g\ge 4$ there is a smallest function $f_g:\mathbb{N}\to\mathbb{N}$ such that every graph of chromatic number at least $f_g(k)$ contains a subgraph of chromatic number $k$ and girth at least $g$. So far, this has only been proved for $g=4$...

Raphael Steiner · 2 citations