论文标题
线性三均匀的超图，没有给定长度的BERGE路径
Linear three-uniform hypergraphs with no Berge path of given length
论文作者
论文摘要
对ERDőS-GALLAI定理的一般超图的扩展进行了充分的研究。在这项工作中，我们证明了线性超图的Erdős-Gallai定理的扩展。特别是，我们表明，$ n $ vertex $ 3 $ 3 $均匀线性超图中的Hyperedges数量，没有长度为$ k $的berge路径，因为子图最多是$ \ frac {（k-1）} {6} {6} {6} n $ for $ k \ geq 4 $。
Extensions of Erdős-Gallai Theorem for general hypergraphs are well studied. In this work, we prove the extension of Erdős-Gallai Theorem for linear hypergraphs. In particular, we show that the number of hyperedges in an $n$-vertex $3$-uniform linear hypergraph, without a Berge path of length $k$ as a subgraph is at most $\frac{(k-1)}{6}n$ for $k\geq 4$.
