可定向曲面上两个地图的交叉数

The Crossing Number of Two-Maps on Orientable Surfaces

中文关键词:  循环图  嵌入  可定向曲面.

英文关键词:crossing number  embedding  orientable surface.

中文摘要:

      本文研究两个单面地图在可定向曲面上的交叉数。通过使用归约方法，我们计算出了两个单面地图及一个单面与一个双面地图在可定向曲面上的交叉数。这就为研究可定向曲面上两个地图的交叉数提供了下界。

英文摘要:

      In this paper, we discuss the crossing numbers of two one-vertex maps on orientable surfaces. By using a reductive method, we give the crossing number of two one-vertex maps with one face on an orientable surface and the crossing number of a one-vertex map with one face and a one-vertex map with two faces on an orientable surface. This provides a lower bound for the crossing number of two general maps on an orientable surface.