LP relaxation of the symmetric TSP problem integrality for n=5

Question

The Dantzig-Fulkerson-Johnson formulation for the symmetric TSP Polytope is given as: $x(\delta(v))=2 \quad \forall v \in V$,
$x(\delta(S))\geq2 \quad \forall \emptyset \subset S \subset V$,
$x \in \{0,1\}^A$.

Also, I see that when there are 5 cities the perfect formulation is
$0 \leq x_e \leq 1 \quad \forall e\in E$,
$x(\delta(v))=2 \quad \forall v \in V$.

I can see that when there are 5 cities, the subtour elimination constraint gets redundant. However, I don't understand how this LP-relaxation gives integral solutions.

Answer 1

Solved it. Grötschel and Padberg (1979) proved that $0 \leq x \leq 1$ defines facets of the TSP polytope when n=5. This fact and redundant subtour elimination constraint gives the perfect formulation.