Edge removal in undirected networks

The edge-removal problem asks whether the removal of a λ-capacity edge from a given network can decrease the communication rate between source-terminal pairs by more than λ. We prove that for undirected networks, removing a λ capacity edge decreases the rate by O(λ). Through previously known reductive arguments, here newly applied to undirected networks, our result implies that the zero-error capacity region of an undirected network equals its vanishing-error capacity region. Whether it is possible to prove similar results for directed networks remains an open question.