Directed Bipartite Graph G U W E Edges Inside U Edges Inside W Every Directed Edge U 7 W U Q37179501

A directed bipartite graph G(U, W, E), has no edges inside U, noedges inside W, and for every directed edge u 7→ w, u ∈ U and w ∈W. A Set cover is a function f : W 7→ U, so that w can be mapped tou only if u 7→ w ∈ E. A directed star is a subset of the edges ofsome vertex u ∈ U.

1. Show that a set cover defines a collection of vertex disjointstars, that contains all of W and vise-versa.

2. Given a star, the vertices in W are called leaves. The sizeof a star

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