We consider the following question of Knuth: given a directed graph $G$ and a root $r$, can the arborescences of $G$ rooted in $r$ be listed such that any two consecutive arborescences differ by only one arc? Such an ordering is called a pivot Gray code and can be formulated as a Hamiltonian path in the reconfiguration graph of the arborescences of $G$ under arc flips, also called flip graph of $G$. We give a positive answer for tournaments and explore several conditions showing that the flip graph of a directed graph may contain no Hamiltonian cycles.

翻译：我们考虑Knuth的如下问题：给定有向图$G$和根节点$r$，能否列出$G$中所有以$r$为根的树状有向生成树，使得任意两个连续的树状有向生成树仅相差一条弧？这种排序称为枢轴格雷码，可表述为在$G$的树状有向生成树关于弧翻转的重构图中的哈密顿路径，该重构图也称为$G$的翻转图。我们对竞赛图给出了肯定答案，并探讨了若干条件，表明有向图的翻转图可能不含哈密顿圈。