The tripartite-circle crossing number of graphs with two small partition classes

Abstract

A tripartite-circle drawing of a tripartite graph is a drawing in the plane, where each part of a vertex partition is placed on one of three disjoint circles, and the edges do not cross the circles. The tripartite-circle crossing number of a tripartite graph is the minimum number of edge crossings among all its tripartite-circle drawings. We determine the exact value of the tripartite-circle crossing number of $K_{a,b,n}$, where $a,b\le 2$.

22 pages, 11 figures. Added new results and revised throughout. Originally appeared in arXiv:1910.06963v1, now removed from arXiv:1910.06963v2