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PreprintarXiv licencearXiv

Weighted Turán densities for hypergraphs

  • David James
  • Bernard Lidický
  • Dhruv Mubayi
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Abstract

Bondy and Tuza generalized the Turán problem for graphs to weighted graphs. Subsequently, Füredi and Kündgen gave a solution in the case of cliques. We consider the weighted Turán problem on hypergraphs and prove the first tight asymptotic result for 3-uniform hypergraphs. Specifically, we determine the weighted Turán density of the generalized triangle F5 = {abc, abd, cde}. We also prove weighted stability results and exact results. Many intriguing open problems remain, the most tantalizing of which is to determine the weighted Turán density of the tetrahedron. Bounds for this density using flag algebras are presented.

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Cite

BibTeXRIS
BibTeX
@misc{james2026weighted,
  title = {{Weighted Turán densities for hypergraphs}},
  author = {David James and Bernard Lidický and Dhruv Mubayi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39085},
  eprint = {2610.39085},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39085},
}
RIS
TY  - UNPB
TI  - Weighted Turán densities for hypergraphs
AU  - David James
AU  - Bernard Lidický
AU  - Dhruv Mubayi
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39085
UR  - https://arxiv.org/abs/2610.39085
AB  - Bondy and Tuza generalized the Turán problem for graphs to weighted graphs. Subsequently, Füredi and Kündgen gave a solution in the case of cliques. We consider the weighted Turán problem on hypergraphs and prove the first tight asymptotic result for 3-uniform hypergraphs. Specifically, we determine the weighted Turán density of the generalized triangle F_5 = {abc, abd, cde}. We also prove weighted stability results and exact results. Many intriguing open problems remain, the most tantalizing of which is to determine the weighted Turán density of the tetrahedron. Bounds for this density using flag algebras are presented.
ER  -