The Crossing Number of Two-Maps on Orientable Surfaces  

作　　者：Yong Xiang WU Hart REN Tu XU 

机构地区：[1]Department of Mathematics Education Resource Center, Ningbo Polytechnic, Zhejiang 315800, P. R. China [2]Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2011年第4期643-648,共6页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.10671073);Science and Technology Commission of Shanghai Municipality (Grant No.07XD14011)

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.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.

关 键 词：crossing number EMBEDDING orientable surface. 

分 类 号：O175.5[理学—数学]