The Weighted Barycenter Drawing Recognition Problem
Peter Eades, Patrick Joseph Healy, Nikola S. Nikolov · arXiv (Cornell University) · 2018
We consider the question of whether a given graph drawing $Γ$ of a triconnected planar graph $G$ is a weighted barycenter drawing. We answer the question with an elegant arithmetic characterisation using the faces of $Γ$. This leads to positive answers when the graph is a Halin graph, and to a polynomial time recognition algorithm when the graph is cubic.