Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation. (8th May 2017)

• Record Type: Journal Article
• Authors: Suebsriwichai, A.; Mouktonglang, T.
• Other Names: Zhang Heping Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2017(2017)
• Publication Date: 2017-05-08
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2017/7640347
• Languages: English
• ISSNs: 1110-757X

Abstract

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.