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Please solve the given question with the correct method, I will give you a thumbs up vote for this. A graph G is bipartite, if

Please solve the given question with the correct method, I will give you a thumbs up vote for this.image text in transcribed

A graph G is bipartite, if its vertex set V can be partitioned into two parts V=LR, so that every edge in G connects one vertex in L and a vertex in R. A perfect matching of a bipartite graph G=(LR,E),L=R, is a set of edges that (1) touches every vertex, and (2) no two edges share a common vertex. The bipartite perfect matching problem asks to decide if a bipartite graph has a perfect matching. A directed graph G=(V,E) is weighted, if there is a function w:EN. Let G=(V,E, w) be a weighted directed graph with two distinct vertices s and t, such that s has no edges coming into it, and t has no edges going out of it. A flow on G from s to t is a function f:EN such that (1) for vV,v=s,t,epointstovf(e)=eleavesvf(e), and (2) for any eE,0f(e)w(e). The flow value of f is eleavessf(e). The maximum flow problem asks, given G=(V,E,w),s,tV satisfying the above, and a number kN, if there exists a flow f on G with flow value k. Give a polynomial-time reduction from the bipartite perfect matching problem to the maximum flow problem. A graph G is bipartite, if its vertex set V can be partitioned into two parts V=LR, so that every edge in G connects one vertex in L and a vertex in R. A perfect matching of a bipartite graph G=(LR,E),L=R, is a set of edges that (1) touches every vertex, and (2) no two edges share a common vertex. The bipartite perfect matching problem asks to decide if a bipartite graph has a perfect matching. A directed graph G=(V,E) is weighted, if there is a function w:EN. Let G=(V,E, w) be a weighted directed graph with two distinct vertices s and t, such that s has no edges coming into it, and t has no edges going out of it. A flow on G from s to t is a function f:EN such that (1) for vV,v=s,t,epointstovf(e)=eleavesvf(e), and (2) for any eE,0f(e)w(e). The flow value of f is eleavessf(e). The maximum flow problem asks, given G=(V,E,w),s,tV satisfying the above, and a number kN, if there exists a flow f on G with flow value k. Give a polynomial-time reduction from the bipartite perfect matching problem to the maximum flow

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