  De Klerk, Pasechnik, and Sotirov give a semidefinite programming constraint
for the Traveling Salesman Problem (TSP) based on the matrix-tree Theorem. This
constraint says that the aggregate weight of all spanning trees in a solution
to a TSP relaxation is at least that of a cycle graph. In this note, we show
that the semidefinite constraint holds for any weighted 2-edge-connected graph
and, in particular, is implied by the subtour elimination constraints of the
subtour elimination linear program. Hence, this semidefinite constraint is
implied by a finite set of linear inequality constraints.
