| The Crossing Number of Two-Maps on Orientable Surfaces |
| Received:December 01, 2009 Revised:November 20, 2010 |
| Key Words:
crossing number embedding orientable surface.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10671073) and Science and Technology Commission of Shanghai Municipality (Grant No.07XD14011). |
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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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