reduction from MAX-CUT to MAX-3-CUT
Hint : Consider  $G '=(V'=V \cup\{w_i|i\in [1,|V|]\},E'=E\cup\{(w_i,v)|v \in V , i\in [1,|V|]\})$ and $k'=|V|^2+k $

Consider a partition of V' in 3 parts, call $P $ the one with the smallest number of nodes in  $V $.

Note that by putting a w in P , if it were not in it, you increase the number of edges in your 3cut. 

Then, note that if all the ws are in the same part, then removing a node of V from that part increases the number of edges in your 3cut.