New Exact Results and Bounds for Bipartite Crossing Numbers of Meshes

  • Matthew C. Newton
  • Ondrej Sýkora
  • Martin Užovič
  • Imrich Vrt’o
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3383)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Matthew C. Newton
    • 1
  • Ondrej Sýkora
    • 1
  • Martin Užovič
    • 2
  • Imrich Vrt’o
    • 3
  1. 1.Department of Computer ScienceLoughborough UniversityLoughboroughUnited Kingdom
  2. 2.Department of Computer ScienceComenius UniversityMlynská dolinaSlovak Republic
  3. 3.Department of InformaticsInstitute of Mathematics, Slovak Academy of SciencesBratislavaSlovak Republic

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