On the size of maximum cut in planar graphs

TL;DR

This paper establishes a lower bound of two-thirds of the edges for the maximum cut size in planar graphs and demonstrates that maximal planar graphs achieve this bound.

Contribution

It proves a tight lower bound for maximum cut size in planar graphs and characterizes maximal planar graphs as extremal cases.

Findings

Maximum cut size in planar graphs is at least 2m/3.

Maximal planar graphs reach this bound.

The bound is tight for maximal planar graphs.

Abstract

We show that the size of maximum cut in a planar graph with $m$ edges is at least $2m/3$. We also show that maximal planar graphs saturate this bound.