Bounding the tripartite?circle crossing number of complete tripartite graphs

A tripartite-circle drawing of a tripartite graph is in the plane, where each part vertex partition placed on one three disjoint circles, and edges do not cross circles. We present upper lower bounds minimum number crossings drawings $K_{m,n,p}$. In contrast to 1- 2-circle drawings, which may attain Harary-Hill bound, our results imply that balanced restricted 3-circle complete are optimal.