ESTIMATION OF THE BIPLANAR CROSSING NUMBERS

This paper is a sequel to our earlier research on biplanar drawings [4] and biplanar crossing numbers [3]. The biplanar crossing number $cr_2$(G) of a graph G is $min\{cr(G_1+cr(G_2)\}$, where $cr$ is the planar crossing number and $G =G_1{\cup}G_2$. In this paper we show that $cr_2(G){\leq}{\frac{3}{8}}cr(G)$.