  We consider the NP-complete problem of tracking paths in a graph, first
introduced by Banik et. al. [3]. Given an undirected graph with a source $s$
and a destination $t$, find the smallest subset of vertices whose intersection
with any $s-t$ path results in a unique sequence. In this paper, we show that
this problem remains NP-complete when the graph is planar and we give a
4-approximation algorithm in this setting. We also show, via Courcelle's
theorem, that it can be solved in linear time for graphs of bounded-clique
width, when its clique decomposition is given in advance.
