Max-Cut and Max-Bisection are NP-hard on unit disk graphs

TL;DR

This paper proves that the Max-Cut and Max-Bisection problems are NP-hard even on unit disk graphs, and explores properties of $\lambda$-precision graphs related to planarity.

Contribution

It establishes NP-hardness of Max-Cut and Max-Bisection on unit disk graphs and analyzes planarity conditions of $\lambda$-precision graphs.

Findings

Max-Cut and Max-Bisection are NP-hard on unit disk graphs

$\lambda$-precision graphs are planar for $\lambda$ > 1 / rac{2}{}

Provides complexity results relevant for geometric graph problems

Abstract

We prove that the Max-Cut and Max-Bisection problems are NP-hard on unit disk graphs. We also show that $\lambda$-precision graphs are planar for $\lambda$ > 1 / \sqrt{2}$.