Separating path systems

Victor Falgas-Ravry, Teeradej Kittipassorn, Dániel Korándi, Shoham Letzter, Bhargav Narayanan

Published 2013-11-20, updated 2016-09-06Version 2

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 $O(n)$ and 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.