It is conjectured that every fullerene graph is hamiltonian.
Jendrol' and Owens proved [J. Math. Chem. 18 (1995), 
pp.~83--90]
that every fullerene graph on $n$ vertices has a cycle
of length at least $4n/5$.
 
In this paper, we study 2-factors of fullerene graphs. As a by-
product, we get an
improvement of a lower bound on the length of the longest 
cycle in a fullerene graph.
We present a constructive proof of the bound $6n/7+2/7$.

IMFM and Univerza v Ljubljani, 
Fakulteta za matematiko in fiziko
Jadranska 21 (the new building)