  An interval graph has interval count $\ell$ if it has an interval model,
where among every $\ell+1$ intervals there are two that have the same length.
Maximum Cut on interval graphs has been found to be NP-complete recently by
Adhikary et al. while deciding its complexity on unit interval graphs (graphs
with interval count one) remains a longstanding open problem. More recently, de
Figueiredo et al. have made an advancement by showing that the problem remains
NP-complete on interval graphs of interval count four. In this paper, we show
that Maximum Cut is NP-complete even on interval graphs of interval count two.
