发表机构
Microsoft; Centro de Informática, Universidade Federal de Pernambuco（微软; 巴西联邦伯南布哥大学计算机中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了Lin、Frankl和Wu提出的猜想：两个不相交的交叉相交3-一致超图（覆盖数为三）的大小乘积尖锐界为100，并通过穷举计算和独立验证给出了具体见证。
AI 中文摘要
Lin、Frankl和Wu证明了两个覆盖数为三的交叉相交3-一致超图的大小乘积至多为121。他们猜想要求族不相交会将尖锐界降低到100。我们证明了这个猜想。较小的族至多有十一条边；在固定它之后，另一个族可以被扩充到其外部3-横截族。按匹配数划分留下一个初等相交情形和两个有限核。我们证明了两种编码和每条剪枝规则的正确性，并且穷举C++20计算给出了族大小4至11的外部阻断最大值分别为21、19、16、14、12、11、10、9。具体见证在Python中独立检查。六个顶点上的一对十条边族达到乘积100。
英文摘要
Lin, Frankl, and Wu proved that the product of the sizes of two cross-intersecting 3-uniform hypergraphs with covering number three is at most 121. They conjectured that requiring the families to be disjoint lowers the sharp bound to 100. We prove this conjecture. The smaller family has at most eleven edges; after fixing it, the other family may be enlarged to its external family of 3-transversals. Splitting by matching number leaves an elementary intersecting case and two finite kernels. We prove the correctness of both encodings and every pruning rule, and exhaustive C++20 computations give the external-blocker maxima 21, 19, 16, 14, 12, 11, 10, 9 for family sizes 4 through 11. Concrete witnesses are checked independently in Python. A pair of ten-edge families on six vertices attains product 100.
Comments8 pages. Computer-assisted proof. The paper-free reproducibility package is available at https://doi.org/10.5281/zenodo.21881247
