Dirac proved that each n-vertex 2-connected graph with minimum degree at least k contains a cycle of length at least \(\min \{2k, n\}\). We consider a hypergraph version of this result. A Berge cycle in a hypergraph is an alternating sequence of distinct vertices and edges \(v_1,e_2,v_2, \ldots , e_c, v_1\) such that \(\{v_i,v_{i+1}\} \subseteq e_i\) for all i (with indices taken modulo c). We prove that for \(n \ge k \ge r+2 \ge 5\), every 2-connected r-uniform n-vertex hypergraph with minimum degree at least \({k-1 \atopwithdelims ()r-1} + 1\) has a Berge cycle of length at least \(\min \{2k, n\}\). The bound is exact for all \(k\ge r+2\ge 5\).

狄拉克证明，每个最小度至少为k的n顶点 2-连通图都包含一个长度至少为\(\min \{2k, n\}\)的环。我们考虑这个结果的超图版本。超图中的伯格循环是不同顶点和边的交替序列\(v_1,e_2,v_2, \ldots , e_c, v_1\)使得\(\{v_i,v_{i+1}\} \subseteq e_i \)对于所有i（索引取模c）。我们证明对于\(n \ge k \ge r+2 \ge 5\)，每个 2-连通r -均匀n -顶点超图的最小度数至少为\({k-1 \atopwithdelims ()r-1 } + 1\)的伯格循环长度至少为\(\min \{2k, n\}\)。对于所有\(k\ge r+2\ge 5\)来说，界限都是精确的。