Bridge position and the representativity of spatial graphs
Bridge position and the representativity of spatial graphs
复制标题
桥梁位置与空间图的代表性
DOI：
10.1016/j.topol.2011.11.026
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
M. Ozawa
中科院分区：
文献类型：
--
作者：
Nagasaki;I;伊藤仁一;H. Endo;M. Ozawa
在本文中，我们考虑包含空间图形的闭曲面。在闭曲面是2-球面的情况下，我们证明了2-球面是等同的，使得它在单圈中与空间图的桥球面相交。在闭曲面不是2-球面的情况下，通过计算压缩圆盘与空间图的交集来定义空间图的不变量。利用这个不变量，我们给出了空间图的桥数的一个下界。
In this paper, we consider closed surfaces which contain spatial graphs. In the case that a closed surface is a 2-sphere, we show that the 2-sphere can be isotoped so that it intersects a bridge sphere for the spatial graph in a single loop. In the case that a closed surface is not a 2-sphere, we define an invariant of a spatial graph by counting the number of intersection of a compressing disk for the closed surface and the spatial graph. By using this invariant, we give a lower bound for the bridge number of a spatial graph.