The Crossing Number of Two-Maps on Orientable Surfaces
Received:December 01, 2009  Revised:November 20, 2010
Key Word: crossing number   embedding   orientable surface.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10671073) and Science and Technology Commission of Shanghai Municipality (Grant No.07XD14011).
Author NameAffiliation
Yong Xiang WU Department of Mathematics Education Resource Center, Ningbo Polytechnic, Zhejiang 315800, P. R. China 
Han REN Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China 
Tu XU Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.04.008
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