  The Graphical Traveling Salesperson Problem (GTSP) is the problem of
assigning, for a given weighted graph, a nonnegative number $x_e$ each edge $e$
such that the induced multi-subgraph is of minimum weight among those that are
spanning, connected and Eulerian. Naturally, known mixed-integer programming
formulations use integer variables $x_e$ in addition to others. Denis Naddef
posed the challenge of finding a (reasonably simple) mixed-integer programming
formulation that has integrality constraints only on these edge variables.
Recently, Carr and Simonetti (IPCO 2021) showed that such a formulation cannot
consist of polynomial-time certifyiable inequality classes unless
$\mathsf{NP}=\mathsf{coNP}$. In this note we establish a more rigorous result,
namely that no such MIP formulation exists at all.
