论文标题
在2-弧形的挖掘中最少的顶点，没有好对
The smallest number of vertices in a 2-arc-strong digraph which has no good pair
论文作者
论文摘要
Bang-Jensen, Bessy, Havet and Yeo showed that every digraph of independence number at most 2 and arc-connectivity at least 2 has an out-branching $B^+$ and an in-branching $B^-$ which are arc-disjoint (such two branchings are called a {\it good pair}), which settled a conjecture of Thomassen for digraphs of independence number 2. They also证明，在最多6个顶点和电弧连接性上的每一个挖掘都至少有2对，并给出了一个2-弧形的Digraph $ d $ d $的示例，其10个顶点的独立编号4，没有很好的配对。他们要求在没有很好的一对的2弧形挖掘物中提供最小的$ n $顶点。在本文中，我们证明最多9个顶点和电弧连接性的每个挖掘都至少有2对，这解决了这个问题。
Bang-Jensen, Bessy, Havet and Yeo showed that every digraph of independence number at most 2 and arc-connectivity at least 2 has an out-branching $B^+$ and an in-branching $B^-$ which are arc-disjoint (such two branchings are called a {\it good pair}), which settled a conjecture of Thomassen for digraphs of independence number 2. They also proved that every digraph on at most 6 vertices and arc-connectivity at least 2 has a good pair and gave an example of a 2-arc-strong digraph $D$ on 10 vertices with independence number 4 that has no good pair. They asked for the smallest number $n$ of vertices in a 2-arc-strong digraph which has no good pair. In this paper, we prove that every digraph on at most 9 vertices and arc-connectivity at least 2 has a good pair, which solves this problem.
