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PreprintCC BY 4.0arXiv

Forbidding r-extension of C4 -- a counterexample of the Anstee-Sali conjecture

  • Richard P. Anstee
  • Attila Sali
  • Pei Wu
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Abstract

In this note we prove forb(n,1r−2× C4)=Θ(nr−1/2), thus providing a series of counterexamples of a 2005 conjecture of the first two authors. Here 1r−2× C4 is the r-extension of the 4-cycle, that is the r-uniform hypergraph of four edges obtained by joining a set of r−2 vertices to each edge of C4. forb(n,F) is the largest number of edges of a simple hypergraph G on n vertices without \emph{trace} (induced subhypergraph) F.

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Cite

BibTeXRIS
BibTeX
@misc{anstee2026forbidding,
  title = {{Forbidding $r$-extension of $C_4$ -- a counterexample of the Anstee-Sali conjecture}},
  author = {Richard P. Anstee and Attila Sali and Pei Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.07646},
  eprint = {2608.07646},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.07646},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Forbidding r-extension of C_4 -- a counterexample of the Anstee-Sali conjecture
AU  - Richard P. Anstee
AU  - Attila Sali
AU  - Pei Wu
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2608.07646
UR  - https://arxiv.org/abs/2608.07646
AB  - In this note we prove forb(n,1_r−2× C_4)=Θ(n^r−1/2), thus providing a series of counterexamples of a 2005 conjecture of the first two authors. Here 1_r−2× C_4 is the r-extension of the 4-cycle, that is the r-uniform hypergraph of four edges obtained by joining a set of r−2 vertices to each edge of C_4. forb(n,F) is the largest number of edges of a simple hypergraph G on n vertices without \emph{trace} (induced subhypergraph) F.
ER  -