∑math20

Combinatorics · Result 171

The hypercube Ramsey conjecture

1 paper

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.

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▶Introduction: the problem and why it mattersin preparation
▶The presented solutionin preparation

Papers 1

First page of The hypercube Ramsey number has linear order

The hypercube Ramsey number has linear order

OpenAI · 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.

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@misc{OAI:The-hypercube-Ramsey-number-has-linear-order-September-23-2026,
  author = {{OpenAI}},
  title = {{The hypercube Ramsey number has linear order}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-hypercube-Ramsey-number-has-linear-order-September-23-2026/paper.pdf}{OAI:The-hypercube-Ramsey-number-has-linear-order-September-23-2026}},
  year = {2026}
}

Formal verification

No Lean formalization is listed for this result yet. The repository notes that unformalized results could have issues.