Separation dimension and degree

• Published in: Mathematical proceedings of the Cambridge Philosophical Society Vol. 170; no. 3; pp. 549 - 558
• Main Authors: SCOTT, ALEX, WOOD, DAVID R.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.05.2021
• Subjects: Graph theory; Hyperplanes; Separation; 05C62

The separation dimension of a graph G is the minimum positive integer d for which there is an embedding of G into ℝd, such that every pair of disjoint edges are separated by some axis-parallel hyperplane. We prove a conjecture of Alon et al. [SIAM J. Discrete Math. 2015] by showing that every graph...