查询词典 contractible graph

Together with some basic knowledge of Linear Algebra, we prove that there exists a polynomial time algorithm for finding the shortest contractible cycle in an locally LEW-embedded graph. 3. By some results of Minor Theorem, we prove the crossing numbers of some circular graphs C(10,4), C(9,3), C(8,3) on the projective plane.

利用C.Thomassen在大边宽嵌入方面的工作，得到了局部大边宽嵌入图的一些性质，再利用线性代数的知识，证明了在局部大边宽条件下存在多项式时间算法可以找到一个图的最短可收缩圈。

This implies the existence of a polynomially bounded algorithm to find a shortest contractible cycle, a shortest separating cycle, and shortest cycle in an embedded graph in the projective plane and answers the open problems raised by Mohar and Thomassen in the case of projective plane embedded graph.

另一方面，通过定义嵌入图的几何对偶图及其相应的嵌入系统，得到几何对偶图中的可分离圈就对应于原图中的割；反之，若几何对偶图中的割在原图中对应于一个圈，那么该圈一定可分离。

We also show that for a fixed surface S, if the face-width of an embedded graph 0 in S is large enough, then there exists a polynomially bounded algorithm to find a shortest contractible cycle in G.

从而在射影平面上解决了Mohar与Thomassen关于是否存在多项式算法寻找短圈的问题。对于一般曲面上嵌入图，只要它的面宽度充分大，那么同样有多项式算法发现最短可收缩圈。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。