Maximum Cut on Interval Graphs of Interval Count Two is NP-complete
Computational Complexity
2024-04-25 v2 Combinatorics
Abstract
An interval graph has interval count if it has an interval model, where among every 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.
Cite
@article{arxiv.2203.06630,
title = {Maximum Cut on Interval Graphs of Interval Count Two is NP-complete},
author = {Alexey Barsukov and Bodhayan Roy},
journal= {arXiv preprint arXiv:2203.06630},
year = {2024}
}