title: Hamilton cycles and paths in fullerenes.
abstract: It has been conjectured that every fullerene, that is, every skeleton of a spherical trivalent graph whose set of faces consists of pentagons and hexagons alone, is Hamiltonian. In this article the validity of this conjecture is explored for the class of leapfrog-fullerenes. It is shown that, given an arbitrary fullerene F, the corresponding leapfrog-fullerene Le(F) contains a Hamilton cycle if the number of vertices of F is congruent to 2 modulo 4 and contains a long cycle missing out only two adjacent vertices, and thus also a Hamilton path, if the number of vertices of F is divisible by 4.
authors.affiliation: University of Ljubljana and University of Primorska, Koper, Slovenia. dragan.marusic@guest.arnes.si
authors.forename: Dragan
authors.initials: D
authors.lastname: Marusic