In Graphic TSP, you are given an unweighted undirected graph $G$ and the goal is to find a shortest tour in $G$ that visits every vertex at least once. Note that this is NOT same as finding a hamiltonian circuit in $G$. My questions are :
What is the complexity of Graphic TSP on bounded treewidth graphs ?
Are there any special cases of Graphic TSP with non-trivial polynomial-time algorithms ?