Transitions of hexangulations on the sphere
Transitions of hexangulations on the sphere
复制标题
球体上六角形的过渡
DOI：
10.1007/s00373-013-1374-0
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发表时间：
2014
影响因子：
0.7
通讯作者：
Naoki Matsumoto
中科院分区：
文献类型：
--
作者：
伊藤 貴弘;高田健司;陳 友根;佐藤 敏文;覚知 豊次;藤本教寛;Naoki Matsumoto
六角图G是一个2-连通简单平面图，使得G的每个面都被一个6-圈所包围。最近证明了任意两个顶点数相同的六角剖分可以通过三个特定的变换相互转化。证明了任意两个分别具有二分拆{B，W}和{B′，W′}的六角化GandG ′，使得|B| = |B′|和|W| = |W′|，可以通过连续应用中的运算相互转换。此外，我们还完整地描述了这四种操作在六角化过渡图中的作用。
AhexangulationGis a 2-connected simple plane graph such that each face ofGis bounded by a 6-cycle. It was recently proved that any two hexangulations with the same number of vertices can be transformed into each other by three specifically defined transformationsand. We prove that any two hexangulationsGandG′ with bipartitions {B,W} and {B′,W′}, respectively, such that |B| = |B′| and |W| = |W′|, can be transformed into each other by successive applications of operations in. Moreover, we completely describe the role of the four operationsandin the transition diagram of hexangulations.