Find a maximum flow in the “standard example” of Sect. 6.5 by applying the Ford-Fulkerson Algorithm but starting with the initial flow given below. Consider the digraph shown in question 11. Interpret...

Find a maximum flow in the “standard example” of Sect. 6.5 by applying the Ford-Fulkerson Algorithm but starting with the initial flow given below.

Consider the digraph shown in question 11. Interpret the arc weights as capacities. Find a maximum flow from the single source (vertex a) to the single sink (vertex b) and a minimum cut.

Show that W is a vertex-cover of G if and only if V \ W is an independent set of vertices in G.

Find a maximum cardinality matching in the bipartite graph given below.