figure bipartite graph give an algorithm to find an augmenting path that permits the maximum flow let be the amount of flow remaining in the residual graph show that the augmenting path produced by the algorithm in part (aadmits path of capacity /|ec show that after |econsecutive iterationsthe total flow remaining in the residual graph is reduced from to at most /ewhere show that |eln iterations suffice to produce the maximum flow find minimum spanning tree for the graph in figure using both prim' and kruskal' algorithms is this minimum spanning tree uniquewhydoes either prim' or kruskal' algorithm work if there are negative edge weights show that graph of vertices can have - minimum spanning trees write program to implement kruskal' algorithm if all of the edges in graph have weights between and | |how fast can the minimum spanning tree be computed figure graph used in exercise