论文标题
翻转飞机跨越路径
Flipping Plane Spanning Paths
论文作者
论文摘要
令$ s $为一般位置设置的平面点，让$ \ Mathcal {p}（s）$为所有平面直线路径的集合，带有顶点套装$ s $。 \ Mathcal {p}（s）$上的路径上的翻转是用$ s $上的另一个边缘$ f $替换$ p $的边缘$ e $ o的操作，从$ s $上方获得了从$ \ mathcal {p}（s）$获得新的有效路径。这是一个长期的开放问题，如果对于每个给定点设置$ s $，则可以通过一系列翻转序列将$ \ Mathcal {p} $从$ \ mathcal {p}（s）$转换为其他任何路径的路径。为了更好地理解这个问题，我们表明足以证明固定第一边缘的平面路径的陈述。此外，我们为特殊类别集的特殊类别提供了正面答案，即车轮组和广义双圆圈（例如，双链和双圆圈）。
Let $S$ be a planar point set in general position, and let $\mathcal{P}(S)$ be the set of all plane straight-line paths with vertex set $S$. A flip on a path $P \in \mathcal{P}(S)$ is the operation of replacing an edge $e$ of $P$ with another edge $f$ on $S$ to obtain a new valid path from $\mathcal{P}(S)$. It is a long-standing open question whether for every given point set $S$, every path from $\mathcal{P}(S)$ can be transformed into any other path from $\mathcal{P}(S)$ by a sequence of flips. To achieve a better understanding of this question, we show that it is sufficient to prove the statement for plane spanning paths whose first edge is fixed. Furthermore, we provide positive answers for special classes of point sets, namely, for wheel sets and generalized double circles (which include, e.g., double chains and double circles).
