On Bipartite Drawings and the Linear Arrangement Problem

The bipartite crossing number problem is studied, and a connection between this problem and the linear arrangement problem is established. It is shown that when the arboricity is close to the minimum degree and the graph is not too sparse, then the optimal number of crossings has the same order of magnitude as the optimal arrangement value times the arboricity. The application of the results to a tree provides for a closed formula which expresses exactly, the optimal number of crossings in terms of the optimal value of the linear arrangement and the degree

• Type: Journal
• Year: 2000
• Where: SIAMCOMP
• Authors: Farhad Shahrokhi, Ondrej Sýkora, László A. Székely, Imrich Vrto
• Keywords: Bipartite Crossing Number, Linear Arrangement, Linear Arrangement Problem, SIAMCOMP 2000