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PreprintarXiv licencearXiv

The O(m2/3) error term for judicious partitions of 3-uniform hypergraphs

  • Siwei Lin
  • Qinghou Zeng
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Abstract

Let k≥2 be a fixed integer. Bollobás and Scott proved that every $3$-uniform hypergraph with m edges admits a partition of its vertex set into k parts such that each part spans at most m/k3+Ok(m6/7) edges. Scott later suggested that the error term should be Ok(m2/3). In this paper, we show that every $3$-uniform hypergraph with m edges admits a partition into k parts such that each part spans at most m/k3+Ok(m2/3) edges, thereby establishing the proposed error term.

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Cite

BibTeXRIS
BibTeX
@misc{lin2026om23,
  title = {{The $O(m^2/3)$ error term for judicious partitions of 3-uniform hypergraphs}},
  author = {Siwei Lin and Qinghou Zeng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09864},
  eprint = {2610.09864},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09864},
}
RIS
TY  - UNPB
TI  - The O(m^2/3) error term for judicious partitions of 3-uniform hypergraphs
AU  - Siwei Lin
AU  - Qinghou Zeng
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09864
UR  - https://arxiv.org/abs/2610.09864
AB  - Let k≥2 be a fixed integer. Bollobás and Scott proved that every $3$-uniform hypergraph with m edges admits a partition of its vertex set into k parts such that each part spans at most m/k^3+O_k(m^6/7) edges. Scott later suggested that the error term should be O_k(m^2/3). In this paper, we show that every $3$-uniform hypergraph with m edges admits a partition into k parts such that each part spans at most m/k^3+O_k(m^2/3) edges, thereby establishing the proposed error term.
ER  -