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2017 Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation
A. Suebsriwichai, T. Mouktonglang
J. Appl. Math. 2017: 1-7 (2017). DOI: 10.1155/2017/7640347

Abstract

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.

Citation

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A. Suebsriwichai. T. Mouktonglang. "Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation." J. Appl. Math. 2017 1 - 7, 2017. https://doi.org/10.1155/2017/7640347

Information

Received: 5 January 2017; Revised: 20 March 2017; Accepted: 10 April 2017; Published: 2017
First available in Project Euclid: 16 June 2017

zbMATH: 07037490
MathSciNet: MR3652895
Digital Object Identifier: 10.1155/2017/7640347

Rights: Copyright © 2017 Hindawi

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