Before revision:  We extend our results to the k-planar crossing number of complete (bipartite ) graphs, for any positive integer k \geq 2. To better understand the relation between crossing numbers and biplanar crossing numbers, we pose a new problem of finding the largest crossing number that implies biplanarity.
After revision:  We extend our results to the k-planar crossing number of complete (bipartite ) graphs, for any positive integer k . We also investigate the relation between crossing numbers and biplanar crossing numbers, we pose a new problem of finding the largest crossing number that implies biplanarity.