We know that the value of the maximum flow is unique in flow networks. However, there...

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We know that the value of the maximum flow is unique in flow networks. However, there can be more than one max-flow function achieving this maximum value. Now, consider a flow network G = (V, E, s, t, c) where we have the following property: 1, 2, V1, V₂ € V: [c(u₁, ₂) 0 c(v₁, v₂) 0 ^ (U₁, U₂) (V₁, V₂) ] ⇒ [c(u₁, U₂) # C(V₁, V₂) ] ^ ‡ Claim A: For such flow networks, there is exactly one max-flow function. Is Claim A true or false? If true, prove it (no partial points if no proof is given). If false, give a counter example by using a flow network of at most 4 nodes on which you need to provide two different max-flow functions (no partial points if no counter example is given or if the counter example uses 5 or more nodes). We know that the value of the maximum flow is unique in flow networks. However, there can be more than one max-flow function achieving this maximum value. Now, consider a flow network G = (V, E, s, t, c) where we have the following property: 1, 2, V1, V₂ € V: [c(u₁, ₂) 0 c(v₁, v₂) 0 ^ (U₁, U₂) (V₁, V₂) ] ⇒ [c(u₁, U₂) # C(V₁, V₂) ] ^ ‡ Claim A: For such flow networks, there is exactly one max-flow function. Is Claim A true or false? If true, prove it (no partial points if no proof is given). If false, give a counter example by using a flow network of at most 4 nodes on which you need to provide two different max-flow functions (no partial points if no counter example is given or if the counter example uses 5 or more nodes).

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