{
  "annotation_id": "852b4a0f-382d-4f3e-8e0c-67f6b2108302",
  "date_created": "2026-02-17T05:53:08.663000Z",
  "date_modified": "2026-02-17T05:53:08.663000Z",
  "file_hash": "4e3a9101e92670dc01722484020fd9d5d5fc9f0fe76433219def870adf733c25",
  "private": false,
  "record": {
    "abstract": "If a family $\\mathcal{F}$ of $k$-element subsets of an $n$-element set is pairwise intersecting, $2k\\leq n$ then $|\\mathcal{F}|\\leq {n-1\\choose k-1}$ holds by the celebrated Erd\\H{o}s-Ko-Rado theorem. But an intersecting family obviously satisfies the condition $${\\ell \\choose 2}\\leq \\sum_{1\\leq i\u003cj\\leq \\ell}|F_i\\cap F_j| $$ for any $\\ell$ distinct members of the family. It has been proved in [5] that even if ${\\ell \\choose 2}$ is replaced by ${\\ell -1 \\choose 2}+1$ the conclusion $|\\mathcal{F}|\\leq {n-1\\choose k-1}$ remains valid for large $n$. However the 1 cannot be omitted, because there is a larger family satisfying that weaker condition. In the present paper we determine the largest size of the family under this weaker condition when $n$ is sufficiently large. All of these are treated in the more general setting of $t$-intersecting families.",
    "arxiv_id": "2601.06871",
    "authors": [
      "Gyula O. H. Katona",
      "Jian Wang"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Nearly Erd\\H{o}s-Ko-Rado theorems",
    "url": "https://arxiv.org/abs/2601.06871",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ffb5247b-3057-43fb-bc66-711a3983233f",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}