Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation
© 2017 A. Suebsriwichai and T. Mouktonglang. The crossing number of graph G is the minimum number of edges crossing in any drawing of G in a plane. In this paper we describe a method of finding the bound of 2-page fixed linear crossing number of G. We consider a conflict graph G′ of G. Then, instead...
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| Main Authors: | , |
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| Format: | Journal |
| Published: |
2017
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| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85019549547&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40873 |
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| Institution: | Chiang Mai University |
| Summary: | © 2017 A. Suebsriwichai and T. Mouktonglang. The crossing number of graph G is the minimum number of edges crossing in any drawing of G in a plane. In this paper we describe a method of finding the bound of 2-page fixed linear crossing number of G. We consider a conflict graph G′ of G. Then, instead of minimizing the crossing number of G, we show that it is equivalent to maximize the weight of a cut of G′. We formulate the original problem into the MAXCUT problem. We consider a semidefinite relaxation of the MAXCUT problem. An example of a case where G is hypercube is explicitly shown to obtain an upper bound. The numerical results confirm the effectiveness of the approximation. |
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