On the anti-Kekule number of fullerenes

The anti-Kekule number of a connected graph G is the smallest number of edges whose removal from G results in a connected subgraph without Kekule structures (perfect matchings). K. Kutnar et al. showed that the anti-Kekule number of leapfrog fullerene graphs is either 3 or 4 [On the anti-Kekule number of leapfrog fullerenes, J. Math. Chem. 45 (2009) 431-441]. In this paper, we show that the anti-Kekule number is always equal to 4 for all fullerene graphs.