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 Ka,b,n, where a, b ≤ 2.