Color-avoiding percolation of random graphs: Between the subcritical and the intermediate regime

Fix a graph G in which every edge is colored in some of k >= 2 colors. Two vertices u and v are CA-connected if u and v may be connected using any subset of k - 1 colors. CA-connectivity is an equivalence relation dividing the vertex set into classes called CA -components.In two recent papers, Rath, Varga, Fekete, and Molontay, and Lichev and Schapira studied the size of the largest CA-component in a randomly colored random graph. The second of these works distinguished and studied three regimes (supercritical, intermediate, and subcritical) in which the largest CA-component has respectively linear, logarithmic, and bounded size. In this short note, we describe the phase transition between the intermediate and the subcritical regime.(c) 2023 Elsevier B.V. All rights reserved.