Evidence item

The quoted arXiv abstract directly states the full parameter range, binomial upper bound, and equality only for a full star. DIRECT_TEXT

Authenticity UNVERIFIED · extraction UNVERIFIED · independence group none (unreviewed) · created seq 24454

Source: The Erdős–Chvátal Simplex Conjecture · locator {} · excerpt hash sha256:12498ccd05f65d4868f4ca1d585608bcf8f82c0ef3425368c32fbdf263d5bbba

We prove the Erdős--Chvátal simplex conjecture across its entire parameter range. If 2≤d<k and (d+1)k≤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.