Fullerene graphs have exponentially many perfect matchings

Frantisek Kardos (1) , Daniel Kral (1) , Jozef Miskuf , Jean-Sébastien Sereni (2, 3)

1 ITI
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
3 KAM - Department of Applied Mathematics (KAM)

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.

Mots clés: fullerene; fullerene graph; perfect matching; Kekulé structure

Domaines: Combinatoire [math.CO]

Frantisek Kardos, Daniel Kral, Jozef Miskuf, Jean-Sébastien Sereni. Fullerene graphs have exponentially many perfect matchings. Journal of Mathematical Chemistry, 2009, 46 (2), pp.443--447. ⟨10.1007/s10910-008-9471-7⟩. ⟨hal-00487070⟩