We study the problem of color-avoiding percolation in a network, i.e., the problem of finding a path that avoids a certain number of colors, associated to vulnerabilities of nodes or links. We show that this problem can be formulated as a self-organized critical problem, in which the asymptotic phase space can be obtained in one simulation. By using the fragment method, we are able to obtain the phase diagram for many problems related to color-avoiding percolation, showing in particular that results obtained for scale-free networks can be recovered using the dilution of the rule on regular lattices.
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