On a variant of Monotone NAE-3SAT and the Triangle-Free Cut problem

Abstract

In this paper we define a restricted version of Monotone NAE-3SAT and show that it remains NP-Complete even under that restriction. We expect this result would be useful in proving NP-Completeness results for problems on $k$-colourable graphs ($k \ge 5$). We also prove the NP-Completeness of the Triangle-Free Cut problem.