The Maximum of the Maximum Rectilinear Crossing Numbers of d-Regular Graphs of Order n

@article{Alpert2009TheMO,
  title={The Maximum of the Maximum Rectilinear Crossing Numbers of d-Regular Graphs of Order n},
  author={Matthew Alpert and Elie Feder and Heiko Harborth},
  journal={Electr. J. Comb.},
  year={2009},
  volume={16}
}
We extend known results regarding the maximum rectilinear crossing number of the cycle graph (Cn) and the complete graph (Kn) to the class of general d-regular graphs Rn,d. We present the generalized star drawings of the d-regular graphs Sn,d of order n where n + d ≡ 1 (mod 2) and prove that they maximize the maximum rectilinear crossing numbers. A star-like drawing of Sn,d for n ≡ d ≡ 0 (mod 2) is introduced and we conjecture that this drawing maximizes the maximum rectilinear crossing numbers… CONTINUE READING