We show that every drawing of Cm×Cn with either the m n-cycles pairwise disjoint or the n m-cycles pairwise disjoint has at least (m?2)n crossings, for every m, n satisfying n?m?3. This supports the long standing conjecture by Harary et al. that the crossing number of Cm×Cn is (m?2)n.
['Gelasio Salazar']
Drawings of Cm×Cn with One Disjoint Family