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PreprintarXiv licencearXiv

Clique-factors in randomly perturbed hypergraphs

  • Yulin Chang
  • Jie Han
  • Patrick Morris
  • Lin Sun
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Abstract

In this paper we establish the following result for clique-factors in randomly perturbed hypergraphs when the cliques are large enough. For integers k ≥ 3 and t≥ t0(k), we show that for every α> 0, there exists C>0 such that for sufficiently large n∈(t+1)ℕ, the union of a k-uniform hypergraph on n vertices with minimum codegree at least αn and a binomial random k-uniform hypergraph H(k)(n,p) with p≥ Cn−t/binomt+1k on the same vertex set contains a Kt+1(k)-factor asymptotically almost surely. The bound on p is asymptotically best possible and extends the graph case, resolved by Balogh, Treglown and Wagner. In particular, we have t0(3)=3, which implies that our result applies to every t≥ 3 for $3$-uniform hypergraphs. Together with the previously established result for perfect matchings, this covers all possible clique sizes for $3$-uniform hypergraphs.

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Cite

BibTeXRIS
BibTeX
@misc{chang2026cliquefactors,
  title = {{Clique-factors in randomly perturbed hypergraphs}},
  author = {Yulin Chang and Jie Han and Patrick Morris and Lin Sun},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41340},
  eprint = {2610.41340},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41340},
}
RIS
TY  - UNPB
TI  - Clique-factors in randomly perturbed hypergraphs
AU  - Yulin Chang
AU  - Jie Han
AU  - Patrick Morris
AU  - Lin Sun
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41340
UR  - https://arxiv.org/abs/2610.41340
AB  - In this paper we establish the following result for clique-factors in randomly perturbed hypergraphs when the cliques are large enough. For integers k ≥ 3 and t≥ t_0(k), we show that for every α> 0, there exists C>0 such that for sufficiently large n∈(t+1)ℕ, the union of a k-uniform hypergraph on n vertices with minimum codegree at least αn and a binomial random k-uniform hypergraph H^(k)(n,p) with p≥ Cn^−t/binomt+1k on the same vertex set contains a K_t+1^(k)-factor asymptotically almost surely. The bound on p is asymptotically best possible and extends the graph case, resolved by Balogh, Treglown and Wagner. In particular, we have t_0(3)=3, which implies that our result applies to every t≥ 3 for $3$-uniform hypergraphs. Together with the previously established result for perfect matchings, this covers all possible clique sizes for $3$-uniform hypergraphs.
ER  -