Extra challenge

[mulliganaceous]

I have been thinking of some extra challenges that might extend the difficulty, posted at the very end

• Graph must be both balanced and have connected components (quite easy given 2 and 3)
• Maxcut may not leave cliques of a certain size within partition. That means, no group of K nodes belonging to the same group belong to a clique.
• Maxcut may not leave independent sets of a certain size.
• Remaining edges must be 3-colorable
• Remaining edges must have Hamiltonian paths within the same group