Fullerene graphs have exponentially many perfect matchings

TL;DR

This paper proves that fullerene graphs, which are special planar cubic graphs with pentagonal and hexagonal faces, have an exponential number of perfect matchings, highlighting their combinatorial richness.

Contribution

The paper establishes the exponential lower bound on the number of perfect matchings in fullerene graphs, a significant advancement in understanding their combinatorial properties.

Findings

Fullerene graphs have exponentially many perfect matchings.

The result advances understanding of fullerene graph structure.

Implications for chemistry and materials science are discussed.

Abstract

A fullerene graph is a planar cubic 3-connected graph with only pentagonal and hexagonal faces. We show that fullerene graphs have exponentially many perfect matchings.