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Given a graph $G=(V,E)$ and a weight function on the edges $w:E\mapsto\RR$,we consider the polyhedron $P(G,w)$ of negative-weight flows on $G$, and get acomplete characterization of the vertices and extreme directions of $P(G,w)$.As a corollary, we show that, unless $P=NP$, there is no output polynomial-timealgorithm to generate all the vertices of a 0/1-polyhedron. This strengthensthe NP-hardness result of Khachiyan et al. (2006) for non 0/1-polyhedra, andcomes in contrast with the polynomiality of vertex enumeration for0/1-polytopes \cite{BL98} [Bussieck and L\"ubbecke (1998)].

Characterization of the Vertices and Extreme Directions of the Negative Cycles Polyhedron and Hardness of Generating Vertices of 0/1-Polyhedra