Color-avoiding percolation on the Erdős–Rényi random graph Lichev, Lyuben Schapira, Bruno ddc:510 We consider a recently introduced model of color-avoiding percolation (abbreviated CA-percolation) defined as follows. Every edge in a graph G is colored in some of k>=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 Erdős–Rényi 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. École normale supérieure de Rennes 2025 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/19859 https://research-explorer.ista.ac.at/download/19859/19875 Lichev L, Schapira B. Color-avoiding percolation on the Erdős–Rényi random graph. <i>Annales Henri Lebesgue</i>. 2025;8:35-65. doi:<a href="https://doi.org/10.5802/ahl.228">10.5802/ahl.228</a> eng info:eu-repo/semantics/altIdentifier/doi/10.5802/ahl.228 info:eu-repo/semantics/altIdentifier/e-issn/2644-9463 info:eu-repo/semantics/altIdentifier/arxiv/2211.16086 info:eu-repo/semantics/openAccess