无4-环链接超图的正则性方法
Regularity method for hypergraphs with $4$-cycle-free links
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中文总结 AI 辅助
该研究将超图正则性方法扩展到顶点链接不含C₄的稀疏3-均匀超图，针对不含K₁,₂,₂且边数为O(|V|^(5/2))的此类超图，建立了七顶点紧圈减一边移除引理的稀疏类似物。
中文摘要 AI 辅助
我们将超图正则性方法扩展到顶点链接为不含C₄的稀疏3-均匀超图，即考虑不含K₁,₂,₂的超图H=(V,E)，这意味着|E|=O(|V|^(5/2))，针对此类超图，我们建立了七顶点紧圈减一边的移除引理的稀疏类似物。
英文摘要
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.
