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The hypercube Ramsey conjecture
Resolves the Burr–Erdős hypercube Ramsey conjecture: the two-color Ramsey number of the n-dimensional cube is . 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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The hypercube Ramsey number has linear order
Sep 23, 2026·paper.pdf
We prove that the two-color Ramsey number of the n-dimensional binary cube is at most , where C is an absolute constant. This resolves positively the hypercube Ramsey conjecture of Burr and Erdős.