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PreprintarXiv licencearXiv

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≤ d<k and (d+1)k≤ dv, then every d-simplex-free family of k-subsets of [v] has at most binomv−1k−1 members, with equality only for a full star.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026erdőschvátal,
  title = {{The Erdős--Chvátal Simplex Conjecture}},
  author = {Jing Huang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14470},
  eprint = {2609.14470},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14470},
}
RIS
TY  - UNPB
TI  - The Erdős--Chvátal Simplex Conjecture
AU  - Jing Huang
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14470
UR  - https://arxiv.org/abs/2609.14470
AB  - 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 binomv−1k−1 members, with equality only for a full star.
ER  -