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Recently the problem of classes of vulnerable vertices (represented bycolors) in complex networks has been discussed, where all vertices with thesame vulnerability are prone to fail together. Utilizing redundant paths eachavoiding one vulnerability (color), a robust color-avoiding connectivity ispossible. However, many infrastructure networks show the problem of vulnerableclasses of \textit{edges} instead of vertices. Here we formulate color-avoidingpercolation for colored edges as well. Additionally, we allow for randomfailures of vertices or edges. The interplay of random failures and possiblecollective failures implies a rich phenomenology. A new form of criticalbehavior is found for networks with a power law degree distribution independentof the number of the colors, but still dependent on existence of the colors andtherefore different from standard percolation. Our percolation framework fillsa gap between different multilayer network percolation scenarios.

Bond and site color-avoiding percolation in scale free networks