N-flips in 4-connected even triangulations on the sphere
N-flips in 4-connected even triangulations on the sphere
复制标题
球体上 4 连通偶数三角剖分中的 N 翻转
DOI：
10.1007/s00373-015-1574-x
复制
发表时间：
2015
影响因子：
0.7
通讯作者：
N. Matsumoto
中科院分区：
文献类型：
--
作者：
Y. Kawasaki;N. Matsumoto
偶三角剖分是一种平面三角剖分，其中每个顶点都有偶数度。众所周知，每一个偶三角剖分都有一个唯一的3-着色，其中的3-着色对顶点的分解称为的三分。Nakamoto et al. （Graph Theory 51:26 - 268, 2006）证明了每两个具有相同三角剖分的偶三角剖分都可以通过翻转（flip）相互转换，其中翻转是将偶三角剖分转换为偶三角剖分的操作。在本文中，我们证明了每两个具有相同三分的4连通偶三角形，除非它们同构于一个广义八面体，否则都可以通过翻转变换成彼此。
Aneven triangulationis a plane triangulation in which each vertex has even degree. It is well known that every even triangulationhas a unique 3-coloring, where the decomposition of the vertices ofby the 3-coloring is called thetripartitionof. Nakamoto et al. (Graph Theory 51:260–268, 2006) proved that every two even triangulations with the same tripartition can be transformed into each other by-flips, where an-flipis an operation transforming an even triangulation into an even triangulation. In this paper, we prove that every two 4-connected even triangulationsandwith the same tripartition can be transformed into each other by-flips unlessoris isomorphic to a generalized octahedron.