3.3. Let J(k) be the graph obtained from H(k) by CF-red, where k 2 ko. We denote the new source and sink by s' and t', respectively. (Note that s and t are retained as usual nodes.) Show that G has a flow f with val(f) = k if and only if the maximum s' – t' flow in J(k) saturates all the edges at s' and t'. Advice: Consider the whole chain of reductions and use the already known facts about LZ-red and CF-red from Lecture Notes 5. You should not need to write much.
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