Schnyder Woods

In two seminal papers published around 1990 Walter Schnyder used a specific partition of the edges of a planar triangulation into three trees to prove two fundamental results.

Schnyder's first theorem. A graph is planar if and only if the dimension of its incidence poset is at most 3.

Schnyder's second theorem. Every planar graph with n vertices admits a straight line drawing on a (n-2)x(n-2) grid.

In recent years it turned out that Schnyder tree partitions, now called Schnyder woods, have many more uses. They appear in the context of enumerative questions and even in algebra. We have contributed to the theory in several papers: