A lower bound for the crossing number ofCm � Cn
Gelasio Salazar · Journal of Graph Theory · 2000
We prove that the crossing number of Cm × Cn is at least (m − 2)n/3, for all m, n such that n ≥ m. This is the best general lower bound known for the crossing number of Cm × Cn, whose exact value has been long conjectured to be (m − 2)n, for 3 ≤ m ≤ n. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 222–226, 2000