  We consider a recently introduced model of color-avoiding percolation defined
as follows. Every edge in a graph $G$ is colored in some of $k\ge 2$ colors.
Two vertices $u$ and $v$ in $G$ are said to be CA-connected if $u$ and $v$ may
be connected using any subset of $k-1$ colors. CA-connectivity defines an
equivalence relation on the vertex set of $G$ whose classes are called
CA-components.
  We study the component structure of a randomly colored Erd\H{o}s-R\'enyi
random graph of constant average degree. We distinguish three regimes for the
size of the largest component: a supercritical regime, a so-called intermediate
regime, and a subcritical regime, in which the largest CA-component has
respectively linear, logarithmic, and bounded size. Interestingly, in the
subcritical regime, the bound is deterministic and given by the number of
colors.

Probability;Combinatorics