The binested inequalities for the symmetric traveling salesman polytope

A class of valid inequalities for the Symmetric Traveling Salesman Polytope is defined on the sets of handles and teeth that are now nested, not of tree structure and no longer restricted to the value one. This new family, the largest known of its kinds so far generalizes the previously defined path, comb, clique tree and hyperstar inequalities and contains some bipartition inqualities as well. The binested inequalities present in this polytope and its graphical relaxation are proven valid. Conditions and conjectures are presented to make this family facet inducing for this specific case.