Bipartizing fullerenes

TL;DR

This paper proves that any fullerene graph can be made bipartite by removing a number of edges proportional to the square root of its vertices, and this bound is proven to be optimal.

Contribution

The paper establishes an asymptotically optimal bound on the number of edges to remove to bipartize fullerene graphs.

Findings

Any fullerene graph on n vertices can be bipartized by removing O(√n) edges.

The bound of O(√n) edges is asymptotically tight.

Provides a method to bipartize fullerene graphs efficiently.

Abstract

A fullerene graph is a cubic bridgeless planar graph with twelve 5-faces such that all other faces are 6-faces. We show that any fullerene graph on n vertices can be bipartized by removing O(sqrt{n}) edges. This bound is asymptotically optimal.