Fractional covering by cuts

We introduce a new graph invariant that measures fractional covering of a graph by cuts. Besides being interested in its own, it is useful for study of cut-continuous mappings (defined in [DeVos, M., J. Nešetřil and A. Raspaud, On flow and tension-continuous maps, KAM-DIMATIA Series 567 (2002)]) and homomorphism. Connections with fractional chromatic number and with bipartite subgraph polytope are pursued.