Author

Jing Huang

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Preprint Sep 2026

The Erd\H{o}s--Chv\'atal Simplex Conjecture

We prove the Erd\H{o}s--Chv\'atal 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.

Jing Huang · 1 citation · ⚡1