  We study a variant of the color-avoiding percolation model introduced by
Krause et al., namely we investigate the color-avoiding bond percolation setup
on (not necessarily properly) edge-colored Erd\H{o}s-R\'{e}nyi random graphs.
We say that two vertices are color-avoiding connected in an edge-colored graph
if after the removal of the edges of any color, they are in the same component
in the remaining graph. The color-avoiding connected components of an
edge-colored graph are maximal sets of vertices such that any two of them are
color-avoiding connected.
  We consider the fraction of vertices contained in color-avoiding connected
components of a given size as well as the fraction of vertices contained in the
giant color-avoiding connected component. Under some mild assumptions on the
color-densities, we prove that these quantities converge and the limits can be
expressed in terms of probabilities associated to edge-colored branching
process trees. We provide explicit formulas for the limit of the normalized
size of the giant color-avoiding component, and in the two-colored case we also
provide explicit formulas for the limit of the fraction of vertices contained
in color-avoiding connected components of a given size.
