论文标题
设置没有简单，Helly Hypergraphs和工会效率家庭的系统
Set systems without a simplex, Helly hypergraphs and union-efficient families
论文作者
论文摘要
我们提供了与集体相关的概念的等效公式，每个子家族都有空的交叉点都有一个有界的子收集与空的交叉点。在此，我们总结了有关此类家庭最大规模的相关问题的进展。 在这项工作中，我们通过应用Karamata的不平等，确定了一个以$ 2 $ 2 $的自我为中心的图表，解决了Tuza问题的边界案例。
We present equivalent formulations for concepts related to set families for which every subfamily with empty intersection has a bounded sub-collection with empty intersection. Hereby, we summarize the progress on the related questions about the maximum size of such families. In this work we solve a boundary case of a problem of Tuza for non-trivial $q$-Helly families, by applying Karamata's inequality and determining the minimum size of a $2$-self-centered graph for which the common neighborhood of every pair of vertices contains a clique of size $q-2$.
