Determine the crossing number of complete bipartite graphs

Determine the crossing number of the complete bipartite graph K_{n,m}, thereby resolving the brick factory problem posed by Turán.

Background

The paper introduces the general problem of determining the minimum number of crossings required in a drawing of a graph, known as its crossing number. It identifies Turán’s brick factory problem as the question of determining the crossing number of the complete bipartite graph K_{n,m}. The problem is presented as a classical unresolved question in graph drawing theory, providing broader context for the paper’s study of how crossings are distributed among edges rather than only their total number.