The Excluded Minors for Isometric Realizability in the Plane

• Main Authors: Fiorini, Samuel, Huynh, Tony, Joret, Gwenaël, Varvitsiotis, Antonios
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2017
• Subjects: Finite metric spaces; Isometric embeddings
• Online Access: https://hdl.handle.net/10356/81454; http://hdl.handle.net/10220/43485
• Institution: Nanyang Technological University

Let $G$ be a graph and $p \in [1, \infty]$. The parameter $f_p(G)$ is the least integer $k$ such that for all $m$ and all vectors $(r_v)_{v \in V(G)} \subseteq \mathbb{R}^m$, there exist vectors $(q_v)_{v \in V(G)} \subseteq \mathbb{R}^k$ satisfying $\|r_v-r_w\|_p=\|q_v-q_w\|_p$ for all $vw\in E(G)....