Geodesic
Sharp Upper Bounds on the Clar Number of Fullerene Graphs
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 155-163

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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.
Keywords: fullerene, Clar number, Clar set, leapfrog transformation 
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Gao, Yang; Zhang, Heping. Sharp Upper Bounds on the Clar Number of Fullerene Graphs. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 155-163. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a12/