Disconnected graphs and extremal bounds for realizable distance orders

Gerardo L. Maldonado, Leonardo Martínez-Sandoval, Miguel Raggi +1

Let $G$ be a graph together with a total order $\prec$ on its edges. We say that $\prec$ is realizable in ${\mathbb{R}}^d$ if there is a placement of the vertices of $G$ in $\mathbb{…