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Keevash-Mubayi Simplex-Cluster Conjecture

The Keevash-Mubayi simplex-cluster conjecture asserts that a family F of k-element subsets of an n-element set with no d-simplex-cluster satisfies

|F|<=(n-1; k-1)

when k>d>=2 and n>k(d+1)/d.

Wu and Feng (2026) reported a proof, also including the boundary case n=k(d+1)/d. Equality holds iff F consists of all k-element subsets containing one fixed element. Wu and Feng (2026) report using ChatGPT to develop and refine the proof.

See also

Simplex-Cluster

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References

Wu, Y. and Feng, L. "The Keevash-Mubayi Simplex-Cluster Conjecture." 6 Oct 2026. https://arxiv.org/abs/2610.08567.

Cite this as:

Weisstein, Eric W. "Keevash-Mubayi Simplex-Cluster Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Keevash-MubayiSimplex-ClusterConjecture.html

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