The Graphical Traveling Salesperson Problem Has No Integer Programming Formulation In The Original Space

The Graphical Traveling Salesperson Problem is the problem of assigning, for a given weighted graph, a nonnegative number x(e) to each edge e such that the induced multi-subgraph is of minimum weight among those that are spanning, connected and Eulerian. Known MIP formulations are based on integer variables x(e). Carr and Simonetti (IPCO 2021) showed that unless NP = coNP, no (reasonable) formulation can have integrality constraints only on x-variables, a challenge posed by Denis Naddef. We establish the same result unconditionally. (C) 2021 Published by Elsevier B.V.