论文标题
Bigraph是超循环的条件
Conditions for a bigraph to be super-cyclic
论文作者
论文摘要
如果每个$ a \ subseteq v（\ mathcal h）$ at $ | a | \ geq 3 $，$ \ Mathcal H $包含一个带有基本顶点套装$ a $的BERGE周期。我们提供了两个自然必要条件，使其具有超级固定图，并表明在几类超图中，这些必要的条件也足够了。特别是，它们足以适用于$δ（\ mathcal h）\ geq \ geq \ max \ {| v（\ mathcal h）|，\ frac {| e（\ mathcal h）| +10} {4} {4} \} $。 我们还考虑了超循环二分图：这些是$（x，y）$ - bigraphs $ g $，以便每$ a \ subseteq x $ with $ | a | \ geq 3 $，$ g $具有循环$ c_a $，这样$ v（c_a）\ cap x = a $。这样的图是超庞然大镜超图的入射图，我们的证明使用了此类图的语言。
A hypergraph $\mathcal H$ is super-pancyclic if for each $A \subseteq V(\mathcal H)$ with $|A| \geq 3$, $\mathcal H$ contains a Berge cycle with base vertex set $A$. We present two natural necessary conditions for a hypergraph to be super-pancyclic, and show that in several classes of hypergraphs these necessary conditions are also sufficient for this. In particular, they are sufficient for every hypergraph $\mathcal H$ with $ δ(\mathcal H)\geq \max\{|V(\mathcal H)|, \frac{|E(\mathcal H)|+10}{4}\}$. We also consider super-cyclic bipartite graphs: those are $(X,Y)$-bigraphs $G$ such that for each $A \subseteq X$ with $|A| \geq 3$, $G$ has a cycle $C_A$ such that $V(C_A)\cap X=A$. Such graphs are incidence graphs of super-pancyclic hypergraphs, and our proofs use the language of such graphs.
