In this paper, we consider maximum possible value for the sum of cardinalities of hyperedges of a hypergraph without a Berge 4-cycle. We significantly improve the previous upper bound provided by Gerbner and Palmer. Furthermore, we provide a construction that slightly improves the previous lower bound.

中文翻译：

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关于Berge的最大尺寸的说明-$C_4$免超图

在本文中，我们考虑了没有Berge 4周期的超图的超边基基数和的最大可能值。我们极大地改善了Gerbner和Palmer提供的先前的上限。此外，我们提供的构造会稍微改善先前的下限。