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This is a Experimental Study study.

October 20, 2025Open Access

Is it easy to regularize a hypergraph with easy links?

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This paper disproves a conjecture on exponential bounds for partitions in hypergraphs, highlighting complexities in 3-graphs.

An improved single exponential bound for $ au$-homogenous partitions in $3$-graphs was established, disproving the previous conjecture.
The findings indicate that not all $3$-graphs can guarantee regular partitions of polynomial size despite having $ au$-homogenous links.
Research explores the conditions under which hypergraphs possess small regular partitions, revealing significant differences between graphs and hypergraphs.
The second result demonstrates that some $3$-graphs require tower-type sizes for regular partitions, even with polynomial-sized $ au$-homogenous links.

Gishboliner et al. (2025) studied this question.

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