An improved bound for the crossing number of Cm×C n: A self-contained proof using mostly combinatorial arguments Article uri icon

abstract

  • We present some surprisingly elementary arguments to prove that for every ∈ > 0, if m is sufficiently large, then the crossing number of the Cartesian product Cm × Cn is at least (0.8 - ∈)mn, for every n ≥ m. The self-contained proof we give involves only one (rather elementary) geometrical result. The rest of the proof involves purely combinatorial arguments. © Springer-Verlag 2004.

publication date

  • 2004-01-01