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.

翻译：区间图具有区间数$\ell$如果它有一个区间模型，使得任意$\ell+1$个区间中必有两个长度相等。Adhikary等人近期发现区间图上的最大割问题是NP完全的，而该问题在单位区间图（区间数为1的图）上的复杂度判定仍是一个长期未决的开放问题。更近期，de Figueiredo等人取得进展，证明该问题在区间数为4的区间图上仍保持NP完全性。本文证明，即便在区间数为2的区间图上，最大割问题也是NP完全的。