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The BFW model introduced by Bohman, Frieze, and Wormald [Random Struct.Algorithms, 25, 432 (2004)] and recently investigated in the framework ofdiscontinuous percolation by Chen and D'Souza [Phys. Rev. Lett., 106, 115701(2011)], is studied on the square and simple-cubic lattices. In two and threedimensions, we find numerical evidence for a strongly discontinuous transition.In two dimensions, the clusters at the threshold are compact with a fractalsurface of fractal dimension $d_f=1.49\pm0.02$. On the simple-cubic lattice,distinct jumps in the size of the largest cluster are observed. We proceed toanalyze the tree-like version of the model, where only merging bonds aresampled, for dimension two to seven. The transition is again discontinuous inany considered dimension. Finally, the dependence of the cluster-sizedistribution at the threshold on the spatial dimension is also investigated.

Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition