František Kardoš & Vesna Andova

12:15 - 13:00 

Speaker: František Kardoš, Université de Bordeaux, France.

Title: One of Barnette's conjectures confirmed: (not only) fullerene graphs are hamiltonian.

Abstract: Fullerene graphs, i.e., 3-connected planar cubic graphs with pentagonal and hexagonal faces, are conjectured to be hamiltonian. This is a special case of a conjecture of Barnette, dating back to the 60s, stating that 3-connected planar cubic graphs with faces of size at most 6 are hamiltonian. We present a computer-assisted proof of the conjecture.

13:15 - 14:00

Speaker: Vesna Andova, St Cyril and Methodius University in Skopje, Macedonia & FIŠ, Novo Mesto.

Title: Bounds on saturation number of fullerene graphs.

Abstract: The saturation number of a graph G is the cardinality of any smallest maximal matching of G, and it is denoted by s(G). Fullerene graphs are cubic planar graphs with exactly twelve 5-faces; all the other faces are hexagons. Here we show that the saturation number for fullerenes on n vertices is essentially  n/3.