关于树的D-平面性的判别准则
On the criteria of D-planarity of a tree
摘要：
设$T$是一棵树，它有一个固定的顶点子集$V^{\ast}$，使得在它上面有一个循环序$C$，并且所有的终端顶点都包含在这个集合中。设$D^{2} = \{(x,y) \in \rr^{2} | x^{2} + y^{2} \leq 1 \}$是一个闭的定向二维圆盘。树$T$称为D-平面的，如果存在满足以下条件$φ(T) \subseteq D^{2}$，$φ(T) \cap \partial D^{2} = φ(V^{\ast})$的嵌入$φ: T \to \rr^{2}$，并且如果$\sharp V^{\ast} \geq 3$，则$φ(V^{\ast})$的循环序$φ(C)$与由$\partial D^{2} \cong S^{1}$的定向生成的循环序一致。
英文摘要：
Let $T$ be a tree with a fixed subset of vertices $V^{\ast}$ such that there is a cyclic order $C$ on it and all terminal vertices are contained in this set. Let $D^{2} = \{(x,y) \in \rr^{2} | x^{2} + y^{2} \leq 1 \}$ be a closed oriented 2--dimensional disk. The tree $T$ is called D-planar if there exists an embedding $φ: T \to \rr^{2}$ which satisfies the following conditions $φ(T) \subseteq D^{2}$, $φ(T) \cap \partial D^{2} = φ(V^{\ast})$ and if $\sharp V^{\ast} \geq 3$ then a cyclic order $φ(C)$ of $φ(V^{\ast})$ coincides with a cyclic order which is generated by the orientation of $\partial D^{2} \cong S^{1}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
