Bollobás, Reed, and Thomason proved every 3‐uniform hypergraph ℋ with m edges has a vertex‐partition V()=V₁⊔V₂⊔V₃ such that each part meets at least edges, later improved to 0.6m by Halsegrave and improved asymptotically to 0.65m+o(m) by Ma and Yu. We improve this asymptotic bound to , which is best possible up to the error term, resolving a special case of a conjecture of Bollobás and Scott.

中文翻译：

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明智地将3分割3一致超图

Bollobás，芦苇，和托马森证明每3-一致超ℋ米边缘具有顶点分区V（）= V ₁ ⊔ V ₂ ⊔ V ₃，使得每个部分满足至少边缘，后提高至0.6米通过Halsegrave和Ma和Yu渐近改善到0.65 m + o（m）。我们改进了到的渐近边界，最大可能直到误差项为止，解决了Bollobás和Scott猜想的特例。