Abstract
We analyze the scaling properties of the largest cluster size for the site percolation problem on small-world graphs. It is shown how the presence of the extra length-scale, the small-world crossover length ξ, influences the fractal dimension D of the spanning cluster. Using the results for dimension d = 2 we find the critical exponent τ governing the cluster size distribution τ ≃ 5/2. This implies that τ is universal and independent of d in agreement with the conjecture by Moore and Newman ( Phys. Rev. E, 62 (2000) 7059).