Bound for the 2‐Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation

A. Suebsriwichai and T. Mouktonglang

Journal of Applied Mathematics, 2017, vol. 2017, issue 1

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.

Date: 2017
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https://doi.org/10.1155/2017/7640347

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2017:y:2017:i:1:n:7640347

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