{
  "abstract": "For a $t$-graph $F$ and an integer $r\\ge t$, the \\emph{$r$-augmentation} $F(r)$ is the $r$-graph obtained by adding the same set of $r-t$ new vertices to every edge of $F$. We investigate the behaviour of the \\emph{Turán density $π(F(r))$}, which is the asymptotically maximum edge density of a large $F(r)$-free $r$-graph, as a function of $r\\to\\infty$. Let $H_k^r$ be the $r$-augmentation of the complete $(k-1)$-graph on $k$ vertices; equivalently, $H_k^r$ is the (unique up to isomorphism) $r$-graph with $r+1$ vertices and $k$ edges. This paper determines the Turán density of each $r$-graph $H_k^r$ within a constant factor and estimates the lower bounds on $π(H_k^r)$ coming from the circular construction of Sidorenko. In particular, it is shown that if $k/\\log r\\to\\infty$ then $π(H_k^r)=(1+o(1))k/r$. Also, we consider augmentations of graphs (that is, the case $t=2$) and prove that $π(F(r))\\ge(\\log r)^{-1-o(1)}/r$ for every 3-chromatic graph $F$, which comes close to the known upper bound $1/r$. Note that, for all other graphs $F$, the function $π(F(r))$ is known to be either identically 0 or uniformly bounded away from 0.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11757",
  "author_total": 3,
  "authors": [
    {
      "name": "Oleg Pikhurko"
    },
    {
      "name": "Jiabao Yang"
    },
    {
      "name": "Xiutao Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4957paxtk2ret.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11757",
  "fulltext_url": null,
  "id": "4957paxtk2ret",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11757",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7221163088",
  "pdf_url": "https://arxiv.org/pdf/2610.11757",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4957paxtk2ret.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.11757",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11757"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Turán densities of hypergraph augmentations",
  "title_text": "Turán densities of hypergraph augmentations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/4957paxtk2ret",
  "venue": "arXiv",
  "versions": []
}