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.

翻译：本文简要阐述了对称旅行商问题（TSP）与定义在单纯关联图上的约束组斯坦纳树问题（cGSTP）之间的结构等价性。给定城市集合V上的完全加权图，我们构建三角形与边之间的二部关联图。选取一组可容许的、盘状三角形集合会诱导出唯一的边界环。在全局连通性与局部正则性约束下，cGSTP中最大化净权重问题完全等价于最小化TSP环游长度问题。