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

TL;DR

This paper introduces a restricted version of Monotone NAE-3SAT that remains NP-Complete and proves the NP-Completeness of the Triangle-Free Cut problem, aiding complexity analyses of graph coloring problems.

Contribution

It establishes NP-Completeness for a restricted Monotone NAE-3SAT variant and the Triangle-Free Cut problem, providing tools for complexity proofs in graph theory.

Findings

Restricted Monotone NAE-3SAT is NP-Complete

Triangle-Free Cut problem is NP-Complete

Results facilitate complexity proofs for k-colorable graphs

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.