Separating edges by linearly many subdivisions

TL;DR

This paper proves that for any two graphs, the edges of one can be separated by a linear number of subdivisions of the other, confirming a conjecture in graph theory.

Contribution

It establishes a linear bound on the number of subdivisions needed to strongly separate edges of any two graphs, confirming a prior conjecture.

Findings

Edges of any graph can be strongly separated by linearly many subdivisions of another graph.

Confirmed a conjecture of Botler and Naia.

Provides a new bound in graph separation theory.

Abstract

We prove that for any two graphs $G$ and $H$, the edges of $G$ can be strongly separated by a collection of linearly many subdivisions of $H$ and single edges. This confirms a conjecture of Botler and Naia.