New exact results and bounds for bipartite crossing numbers of meshes

Authors:
Matthew C. Newton;Ondrej Sýkora;Martin Užovič;Imrich Vrt'o
Affiliations:
Department of Computer Science, Loughborough University, Loughborough, Leicestershire, United Kingdom;Department of Computer Science, Loughborough University, Loughborough, Leicestershire, United Kingdom;Department of Computer Science, Comenius University, Mlynská dolina, Bratislava, Slovak Republic;Department of Informatics, Institute of Mathematics, Slovak Academy of Sciences, Bratislava, Slovak Republic
Venue:
GD'04 Proceedings of the 12th international conference on Graph Drawing
Year:
2004

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Abstract

The bipartite crossing number of a bipartite graph is the minimum number of crossings of edges when the partitions are placed on two parallel lines and edges are drawn as straight line segments between the lines. We prove exact results, asymtotics and new upper bounds for the bipartite crossing numbers of 2-dimensional mesh graphs. We especially show that bcr(P6× Pn)=35n–47, for n≥ 7.