Instability of Bose-Einstein condensation into the one-particle ground state on quantum graphs under repulsive perturbations

In this paper we investigate Bose-Einstein condensation into the one-particle ground state in interacting quantum many-particle systems on graphs. We extend previous results obtained for particles on an interval and show that even arbitrarily small repulsive two-particle interactions destroy the condensate in the one-particle ground state present in the non-interacting Bose gas. Our results also cover singular two-particle interactions, such as the well-known Lieb-Liniger model, in the thermodynamic limit.