Contents Online

# Journal of Combinatorics

## Volume 5 (2014)

### Number 3

### Separating path systems

Pages: 335 – 354

DOI: http://dx.doi.org/10.4310/JOC.2014.v5.n3.a4

#### Authors

#### Abstract

We study separating systems of the edges of a graph where each member of the separating system is a path. We conjecture that every $n$-vertex graph admits a separating path system of size linear in $n$ and we prove this in certain interesting special cases. In particular, we establish this conjecture for random graphs and graphs with linear minimum degree. We also obtain tight bounds on the size of a minimal separating path system in the case of trees.