A Structural Equivalence of Symmetric TSP to a Constrained Group Steiner Tree Problem

We present a brief structural equivalence between the symmetric TSP and
a constrained Group Steiner Tree Problem (cGSTP) defined on a simplicial incidence graph.
Given the complete weighted graph on the city set V, we form the bipartite incidence graph between triangles and edges.
Selecting an admissible, disk-like set of triangles induces a unique boundary cycle.
With global connectivity and local regularity constraints, maximizing net weight in the cGSTP is exactly
equivalent to minimizing the TSP tour length.