New exact results and bounds for bipartite crossing numbers of meshes

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. © Springer-Verlag Berlin Heidelberg 2004.