Turán problems with bounded matching number in k-uniform hypergraphs

@misc{liu2026turán,
  title = {{Turán problems with bounded matching number in $k$-uniform hypergraphs}},
  author = {Jialin Liu and Mingyang Guo and Xiumei Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.24353},
  eprint = {2609.24353},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24353},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Turán problems with bounded matching number in k-uniform hypergraphs
AU  - Jialin Liu
AU  - Mingyang Guo
AU  - Xiumei Wang
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.24353
UR  - https://arxiv.org/abs/2609.24353
AB  - For a family ℱ of k-graphs, ex_k(n,ℱ) denotes the maximum number of edges in an n-vertex ℱ-free k-graph. Let M_s+1^k denote a matching of size s+1 in k-uniform hypergraphs. Recently, Alon and Frankl (JCTB, 2024) determined ex_2(n,{M_s+1^2,K_ℓ+1}) for all n≥ 2s+1 and ℓ≥ 2. For every non-bipartite graph F, Gerbner (JGT, 2024) determined ex_2(n,{M_s+1^2,F}) for sufficiently large n. In this paper, we investigate this problem for different ranges of the matching parameter. First we prove that for every graph F with χ(F)>3, there exist constants β>0 and s_0 such that ex_2(n,{M^2_s+1, F})=ex_2(2s+1,F) for max{s_0,n/2−βn}<s<n/2. For integers ℓ≥ k≥3, let 𝒦_ℓ+1^k be the family of all k-graphs F with at most binomℓ+12 edges for which there is an (ℓ+1)-set L such that every pair of vertices of L is covered by an edge of F, and let H_ℓ+1^k be the k-uniform hypergraph obtained from the complete graph K_ℓ+1 by enlarging each edge with a set of k−2 new vertices, which is a member of 𝒦_ℓ+1^k. We determine ex_k(n,𝒦_ℓ+1^k∪{M_s+1^k}) for s< n/(8(k−1)^k−2(ℓ−1)^3). For sufficiently large s, we also determine ex_k(n,{M_s+1^k,H_ℓ+1^k}) for n/k−βn<s≤ (n−k)/k and s< n/(8(k−1)^k−2(ℓ−1)^3).
ER  -