  The computational complexity of the MaxCut problem restricted to interval
graphs has been open since the 80's, being one of the problems proposed by
Johnson on his Ongoing Guide to NP-completeness, and has been settled as
NP-complete only recently by Adhikary, Bose, Mukherjee and Roy. On the other
hand, many flawed proofs of polynomiality for MaxCut on the more restrictive
class of unit/proper interval graphs (or graphs with interval count 1) have
been presented along the years, and the classification of the problem is still
unknown. In this paper, we present the first NP-completeness proof for MaxCut
when restricted to interval graphs with bounded interval count, namely graphs
with interval count 4.
