We denote by E [X,Y] the set of edges of G with one end in X and the other end in Y and by e (X,Y) their number.

2.5.4 Let G be a loopless graph, and let X and Y be subsets of V. a) Show that: b) Deduce the following submodular inequality for degrees of sets of vertices. c) State and prove a directed analogue of this submodular inequality 2.5.4 Let G be a loopless graph, and let X and Y be subsets of V. a) Show that: b) Deduce the following submodular inequality for degrees of sets of vertices. c) State and prove a directed analogue of this submodular inequality