A Note on Schnyder's Theorem

TL;DR

This paper provides an alternative proof of Schnyder's Theorem, establishing that a graph's incidence poset has dimension at most three if and only if the graph is planar, thus offering new insights into graph planarity and poset dimension.

Contribution

The paper introduces a new proof technique for Schnyder's Theorem, enhancing understanding of the relationship between graph planarity and poset dimension.

Findings

Incidence poset of a planar graph has dimension at most three

Non-planar graphs have incidence posets with dimension greater than three

Alternative proof simplifies understanding of Schnyder's Theorem

Abstract

We give an alternate proof of Schnyder's Theorem, that the incidence poset of a graph $G$ has dimension at most three if and only if $G$ is planar.