Abstract Forty years ago, Kleitman considered the numbers of crossings in good planar drawings of the complete bipartite graph ${K_{m,n}}$. Among other things, he ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

A drawing of a graph G in the plane has the vertices represented by distinct points and the edges represented by polygonal lines joining their endpoints such that: no edge contains a vertex other than ...