论文标题
三连接的超图和两部分图中的最长循环
Longest cycles in 3-connected hypergraphs and bipartite graphs
论文作者
论文摘要
用超图的语言，我们的主要结果是狄拉克类型的绑定：我们证明，每$ 3 $连接的hypergraph $ h $都带有$δ（h）\ geq \ geq \ max \ max \ {| v（h）|，\ frac {| e（h）| e（h） 这是尖锐的，并完善了杰克逊（Jackson）从1981年开始的猜想（用两分图的语言）。我们的证明是用两分图的语言，因为每个超图的发生率图是两部分。
In the language of hypergraphs, our main result is a Dirac-type bound: we prove that every $3$-connected hypergraph $H$ with $ δ(H)\geq \max\{|V(H)|, \frac{|E(H)|+10}{4}\}$ has a hamiltonian Berge cycle. This is sharp and refines a conjecture by Jackson from 1981 (in the language of bipartite graphs). Our proofs are in the language of bipartite graphs, since the incidence graph of each hypergraph is bipartite.
