Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 54 min ago
PreprintarXiv licencearXiv

Codegree-Constrained Turán Problems for F5 and Its Blow-ups

  • Yupei Li
  • Linyuan Lu
Open at sourcePDFDOICite

Abstract

Let F5 denote the $3$-uniform hypergraph with edge set {abc,abd,cde}. For a hypergraph property 𝒫, let ex𝒫(n,F5) be the maximum number of edges in an n-vertex F5-free $3$-uniform hypergraph satisfying 𝒫. Let Δ2(H) denote the maximum codegree of a pair of vertices in a $3$-uniform hypergraph H. We determine the exact value of exΔ2≥ m(n,F5) when m is bounded away from n/3 by a fixed positive proportion. More precisely, for every constant c∈ (1/3,1), there exists n0 such that for all n≥ n0 and m=cn, exΔ2≥ m(n,F5) = m⌈(n−m)/2⌉ ⌊(n−m)/2⌋. The unique extremal hypergraph is the complete tripartite $3$-graph K3m,⌈ (n−m)/2⌉,⌊ (n−m)/2⌋. We also prove the corresponding exact result for the blow-ups F5t, together with stability theorems showing that every near-extremal configuration is close to the relevant tripartite construction.

Related

  1. Characterizing $3$-graphs with Degenerate Codegree Turán Density
    Dylan King, Simón Piga, Marcelo Sales +1
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  2. Turán-type extremal problems for unbalanced signed graphs
    Linfeng Xie, Keheng Zhu, Xiaogang Liu
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  3. The signless Laplacian spectral Turán problems for disjoint triangles
    Ming-Zhu Chen, Ya-Lei Jin, Peng-Li Zhang
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  4. Generalized Turán problems for shorter even cycles
    Zhen Liu, Chuanshu Wu
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. NP-Hardness of Generalized-Turán Graph Modification Problems
    Lior Gishboliner, Yevgeny Levanzov, Asaf Shapira
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{li2026codegreeconstrained,
  title = {{Codegree-Constrained Turán Problems for $F_5$ and Its Blow-ups}},
  author = {Yupei Li and Linyuan Lu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12905},
  eprint = {2610.12905},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12905},
}
RIS
TY  - UNPB
TI  - Codegree-Constrained Turán Problems for F_5 and Its Blow-ups
AU  - Yupei Li
AU  - Linyuan Lu
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.12905
UR  - https://arxiv.org/abs/2610.12905
AB  - Let F_5 denote the $3$-uniform hypergraph with edge set {abc,abd,cde}. For a hypergraph property 𝒫, let ex_𝒫(n,F_5) be the maximum number of edges in an n-vertex F_5-free $3$-uniform hypergraph satisfying 𝒫. Let Δ_2(H) denote the maximum codegree of a pair of vertices in a $3$-uniform hypergraph H. We determine the exact value of ex_Δ_2≥ m(n,F_5) when m is bounded away from n/3 by a fixed positive proportion. More precisely, for every constant c∈ (1/3,1), there exists n_0 such that for all n≥ n_0 and m=cn, ex_Δ_2≥ m(n,F_5) = m⌈(n−m)/2⌉ ⌊(n−m)/2⌋. The unique extremal hypergraph is the complete tripartite $3$-graph K^3_m,⌈ (n−m)/2⌉,⌊ (n−m)/2⌋. We also prove the corresponding exact result for the blow-ups F_5^t, together with stability theorems showing that every near-extremal configuration is close to the relevant tripartite construction.
ER  -