Year: 2026
Type: preprint
Abstract: Let $k\ge2$ 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.
Source: arXiv (Cornell University)
Authors: Lin, Siwei, Zeng, Qinghou
Institution: Fuzhou University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G8874812387
OpenAlex ID: W7220911058