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arXiv · 2608.24740

Regularity method for hypergraphs with $4$-cycle-free links

Ayush Basu·Christian Reiher·Vojtěch Rödl·Mathias Schacht
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Abstract

We extend the hypergraph regularity method to sparse $3$-uniform hypergraphs whose vertex links are $C_4$-free. In other words, we consider hypergraphs $H=(V,E)$ that are $K_{1,2,2}$-free, which implies that $|E|=O(|V|^{5/2})$. For such hypergraphs we establish a sparse analogue of the removal lemma for the tight cycle on seven vertices minus an edge.

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Ayush Basu, Christian Reiher, Vojtěch Rödl, Mathias Schacht. 2026-08-25. Regularity method for hypergraphs with $4$-cycle-free links. https://arxiv.org/abs/2608.24740

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