论文标题
汉密尔顿循环在密集的常规挖掘和定向图中
Hamilton Cycles in Dense Regular Digraphs and Oriented Graphs
论文作者
论文摘要
我们证明，每一个$ \ varepsilon> 0 $都存在$ n_0 = n_0（\ varepsilon）$，使得$ n> n_0 $ vertices上的每个常规图形和度量至少至少$（1/4 + \ varepsilon）N $都有汉密尔顿周期。这建立了1981年从杰克逊（Jackson）的猜想的大概版本。我们还建立了与库恩（Kühn）和奥斯图斯（Osthus）的猜想有关的结果，该猜想是关于具有适当程度和连通性条件的常规定向图的汉密尔顿性。
We prove that for every $\varepsilon > 0$ there exists $n_0=n_0(\varepsilon)$ such that every regular oriented graph on $n > n_0$ vertices and degree at least $(1/4 + \varepsilon)n$ has a Hamilton cycle. This establishes an approximate version of a conjecture of Jackson from 1981. We also establish a result related to a conjecture of Kühn and Osthus about the Hamiltonicity of regular directed graphs with suitable degree and connectivity conditions.
