We know that finding a max cut for weighted graphs is NP-Complete. I am trying to find a proof showing that even for graphs with just unit weights (every edge has weight 1) it is still NP-Complete. I've looked at the proofs reducing 3 NAESAT and vertex cover problems to max cut. But in those proofs we get weighted graphs for which we find max cuts. If someone could point me in the right direction I would appreciate it.

  • 2
    $\begingroup$ If you are stuck with your homework then you should rather ask your teacher for a hint. $\endgroup$
    – Gamow
    Dec 27, 2016 at 11:18
  • 3
    $\begingroup$ I am not a student. I am a teacher and this wasn't a HW question. Well at least not one I assigned. $\endgroup$ Dec 27, 2016 at 11:25
  • $\begingroup$ This is clearly not a research level question. $\endgroup$
    – ivmihajlin
    Dec 30, 2016 at 23:28

1 Answer 1


Yes, Max-Cut is still NP-complete in unweighted graphs.

This is explained in pretty much every survey article on tthe Max-Cut problem, and in many texbooks (as for instance "Computational Complexity" by C.H. Papadimitriou). The first proof goes back to the year 1976:

M.R. Garey, D.S. Johnson, L. Stockmeyer
Some simplified NP-complete graph problems
Theoretical Computer Science 1 (1976), pp 237-267


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