Is it "easier" to find the optimal solution to the travelling salesman problem of size $n$ given that you have the optimal solution for size $n-1$?

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Provided with a complete graph $G = (V, E)$ where $|V| = n$, and an optimal solution that minimizes the travel cost for the subgraph $G' = (V', E')$, where $V' \subset V,\, |V'| = n-1$. Is it then computationally "easier" to find the optimal solution for the TSP of $G$?