Resolves the Burr–Erdős hypercube Ramsey conjecture: the two-color Ramsey number of the n-dimensional cube is \Theta(2^n). Thus every red-blue coloring of a complete graph on a universal constant times the cube's number of vertices contains a monochromatic copy of the cube.
Manuscript
The hypercube Ramsey number has linear order
September 23, 2026 · source · cite as \cite{OAI:The-hypercube-Ramsey-number-has-linear-order-September-23-2026}
We prove that the two-color Ramsey number of the n-dimensional binary cube is at most C2^n, where C is an absolute constant. This resolves positively the hypercube Ramsey conjecture of Burr and Erdős.
Result 171 · Combinatorics. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md