Complete inequality description of the Hamiltonian cycle polytope

Determine the complete set of linear inequalities defining the symmetric traveling salesman polytope (Hamiltonian cycle polytope) of the complete graph $K_n$.

Background

The paper distinguishes the symmetric traveling salesman polytope $P_{\mathrm{STSP},n}$, defined as the convex hull of incidence vectors of Hamiltonian cycles of $K_n$, from the subtour elimination (Held--Karp) relaxation polytope $P_{\mathrm{SEP},n}$. Although the latter has a standard tractable description by degree and subtour inequalities, it is generally a strict relaxation of the Hamiltonian cycle polytope. A complete inequality description of $P_{\mathrm{STSP},n}$ would characterize exactly which edge-weight vectors lie in the convex hull of Hamiltonian cycles, rather than merely in the Held--Karp relaxation.