The bandwidth of a graph is the minimum, over vertex labelings using distinct integers, of the maximum diierence between labels of adjacent ver-tices. Let f(n) denote the maximum sum of the bandwidths of complementary n-vertex graphs. Chinn, Chung, Erd} os, and Graham 3] proved the existence of constants c 1 ; c 2 such that 2n ? c 2 log n f(n) 2n ? c 1 log n. We sharpen this to 2n ? 8 log 2 n ?...