selected become isolated points of $G^{(1)}$. They remain isolated for the rest of the process. Iterate the procedure and define $G^{(2)},G^{(3)},\cdots$ until a graph without leaves is obtained.

In the proof given in the appendix that the core is well-defined, the argument in step $\mathbf{3c}$ implies in particular that leaf removals that take place in distinct bunches of a graph commute. It implies that the global leaf removal process leads to same core and number of isolated points as any step by step leaf removal process.

While the global leaf removal process is convenient for analytical computations, the step by step leaf removal process is easier to implement on the computer.

Core percolation: infinite $N$ results {#sec:coreperco}
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The global leaf removal process allows to compute the most salient characteristics of the leaf removal process, the functions $i(\alpha)$, $c(\alpha)$ and $l(\alpha)$. Remember that by definition, the number of isolated points after leaf removal is $Ni(\alpha)+o(N)$, the number of vertices in the core is $N_c=Nc(\alpha)+o(N)$, and the number of edges in the core is $L_c=Nl(\alpha) +o(N)$. The clue is an enumeration of all the configurations on the random graph that contribute extensively to the fundamental events in the global leaf removal 