The Clar number of a fullerene graph with n vertices is bounded above by ⌊n/6⌋ − 2 and this bound has been improved to ⌊n/6⌋ − 3 when n is congruent to 2 modulo 6. We can construct at least one fullerene graph attaining the upper bounds for every even number of vertices n ≥ 20 except n = 22 and n = 30.
@article{bwmeta1.element.doi-10_7151_dmgt_2013,
author = {Yang Gao and Heping Zhang},
title = {Sharp Upper Bounds on the Clar Number of Fullerene Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {38},
year = {2018},
pages = {155-163},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_2013}
}
Yang Gao; Heping Zhang. Sharp Upper Bounds on the Clar Number of Fullerene Graphs. Discussiones Mathematicae Graph Theory, Tome 38 (2018) pp. 155-163. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_2013/