Robust flow model gap conjecture

Consider an instance of the robust flow models with uncertainty parameter $\Gamma\in\mathbb{N}$. Let $f^*_{\textit{gm}}$, $f^*_{\textit{am}}$, and $f^*_{\textit{pm}}$ denote the optimal values of the general, arc, and path models, respectively.

Robust flow gap conjecture. For any $\Gamma\in\mathbb{N}$, the inequalities

$$f^*_{\textit{gm}}\leq (\Gamma+1)f^*_{\textit{pm}}$$

and

$$f^*_{\textit{am}}\leq (\Gamma+1)f^*_{\textit{pm}}$$

hold on every instance.

These inequalities conjecturally give tight upper bounds on how much the robust general and arc models can outperform the robust path model. The conjecture is motivated by examples and by tightness on directed acyclic graphs with $\Gamma=1$; no general resolution is supplied.