Crossing numbers of meshes

  • Farhad Shahrokhi
  • Ondrej Sýkora
  • László A. Székely
  • Imrich Vrt'o
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1027)


We prove that the crossing number of the cartesian product of 2 cycles, Cm× Cn, m≤n, is of order Ω(mn), improving the best known lower bound. In particular we show that the crossing number of Cm×Cn is at least mn/90, and for n=m, m+1 we reduce the constant 90 to 6. This partially answers a 20-years old question of Harary, Kainen and Schwenk [3] who gave the lower bound m and the upper bound (m−2)n and conjectured that the upper bound is the actual value of the crossing number for Cm×Cn. Moreover, we extend this result to k≥3 cycles and paths, and obtain such lower and upper bounds on the crossing numbers of the corresponding meshes, which differ by a small constant only.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Farhad Shahrokhi
    • 1
  • Ondrej Sýkora
    • 2
  • László A. Székely
    • 3
  • Imrich Vrt'o
    • 2
  1. 1.Department of Computer ScienceUniversity of North TexasDentonUSA
  2. 2.Institute for InformaticsSlovak Academy of SciencesBratislavaSlovak Republic
  3. 3.Department of Computer ScienceEötvös UniversityBudapestHungary

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