Fullerene graphs have exponentially many perfect matchings

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.

7 pages, 3 figures

Cited by in corpus (9)

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• Extremal fullerene graphs with the maximum Clar number
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• Bipartizing fullerenes
• The saturation number of carbon nanocones and nanotubes
• Nice vertices in cubic graphs
• On the saturation number of graphs
• Asymptotic enumeration of perfect matchings in $m$-barrel fullerene graphs
• 2-Resonant fullerenes