| A Nonconvex Nonorientable Crossing Number Sequence |
| Received:October 30, 2008 Revised:May 17, 2009 |
| Key Words:
crossing number embedding non-orientable surface.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10671073) and the Science and Technology Commission of Shanghai Municipality (Grant No.07XD14011). |
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| Abstract: |
| It is well known that finding the crossing number of a graph on nonplanar surfaces is very difficult. In this paper we study the crossing number of the circular graph $C(10,4)$ on the projective plane and determine the nonorientable crossing number sequence of $C(10,4)$. On the basis of the result, we show that the nonorientable crossing number sequence of $C(10,4)$ is not convex. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.06.005 |
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