This letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd?s and Rényi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two major results are found: i) For any specific m, the critical percolation point scales with the average degree of the network while its exponent associated with m is bounded by-1 and ~-0.5. ii) Discontinuous percolation could occur on sparse networks if and only if m approaches infinite. These results not only generalize some conclusions of ordinary percolation but also provide new insights into the network robustness.
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