For TSP with triangle inequality, Approx-TSP-Tour is an approximation algorithm
with a ratio bound of 2.
Removing an edge from a tour yields a spanning tree.
Thus, if H* is the optimal tour and T is a MST(G), then c(T) c(H*).
Consider a full walk W of a MST with cost c(W).
W is not a tour, but by triangle inequality, we can change
y, without increasing cost to yield
approximate tour H. Or, use the pre-order traversal of the MST.