We study the reconfiguration of plane spanning trees on point sets in the plane in convex position, where a reconfiguration step (flip) replaces one edge with another, yielding again a plane spanning tree. The flip distance between two trees is then the minimum number of flips needed to transform one tree into the other. We study structural properties of shortest flip sequences. The folklore happy edge conjecture suggests that any edge shared by both the initial and target tree is never flipped in a shortest flip sequence. The more recent parking edge conjecture, which would have implied the happy edge conjecture, states that there exist shortest flip sequences which use only edges of the start and target tree, and edges in the convex hull of the point set. Finally, another conjecture that is implicit in the literature is the reparking conjecture which states that no edge is flipped more than twice. Essentially all recent flip algorithms respect these three conjectures and the properties they imply. We study cases in which the latter two conjectures hold and disprove them for the general setting. (Shortened abstract due to arXiv restrictions.)

翻译：我们研究平面上凸位置点集上平面生成树的重构问题，其中每次重构步骤（翻转）将一条边替换为另一条边，并再次产生一棵平面生成树。两棵树之间的翻转距离即为将一棵树转换为另一棵树所需的最小翻转次数。我们研究最短翻转序列的结构性质。广为流传的"快乐边猜想"认为，初始树和目标树共有的任何边在最短翻转序列中永远不会被翻转。较近期的"停车边猜想"（该猜想若成立则可推出快乐边猜想）指出，存在仅使用起点树和目标树的边、以及点集凸包中的边的最短翻转序列。最后，文献中隐含的另一个猜想是"重新停车猜想"，该猜想认为没有边会被翻转超过两次。本质上，所有近期的翻转算法都遵循这三个猜想及其所蕴含的性质。我们研究后两个猜想成立的情形，并在一般设定下证伪了它们。（因arXiv限制，摘要有所缩短。）