Recall that TSP is an optimization problem where we seek the shortest possible route, while MST is a decision problem where we only need to determine if a spanning tree of a certain weight exists.

Consider the nature of verification: For MST, given a candidate solution, we can efficiently verify its correctness, but for TSP, verifying an optimal solution is non-trivial due to the lack of a clear "yes/no" structure.

Examine the role of approximation: While MST has well-known polynomial-time approximation algorithms (e.g., Kruskal's), TSP lacks such guarantees for general cases, highlighting its computational hardness even in approximate settings.