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arXiv · 2609.14470

The Erdős--Chvátal Simplex Conjecture

Jing Huang
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Abstract

We prove the Erdős--Chvátal simplex conjecture across its entire parameter range. If $2\le d<k$ and $(d+1)k\le dv$, then every $d$-simplex-free family of $k$-subsets of $[v]$ has at most $\binom{v-1}{k-1}$ members, with equality only for a full star.

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Jing Huang. 2026-09-13. The Erdős--Chvátal Simplex Conjecture. https://arxiv.org/abs/2609.14470

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