On k-planar crossing numbers

Authors:
Farhad Shahrokhi;Ondrej Sýkora;László A. Székely;Imrich Vrt'o
Affiliations:
Department of Computer Science, University of North Texas, P.O. Box 13886, Denton, TX 76203-3886, USA;Department of Computer Science, Loughborough University, Loughborough, LE11 3TU, UK;Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA;Institute of Mathematics, Slovak Academy of Sciences, Dúbravská 9, 841 04 Bratislava, Slovak Republic
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

The k-planar crossing number of a graph is the minimum number of crossings of its edges over all possible drawings of the graph in k planes. We propose algorithms and methods for k-planar drawings of general graphs together with lower bound techniques. We give exact results for the k-planar crossing number of K"2"k"+"1","q, for k=2. We prove tight bounds for complete graphs. We also study the rectilinear k-planar crossing number.