The Weighted Barycenter Drawing Recognition Problem

Abstract

We consider the question of whether a given graph drawing $\Gamma$ of a triconnected planar graph $G$ is a weighted barycenter drawing. We answer the question with an elegant arithmetic characterisation using the faces of $\Gamma$. This leads to positive answers when the graph is a Halin graph, and to a polynomial time recognition algorithm when the graph is cubic.

Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018)