A note on non-isomorphic edge-color classes in random graphs

Abstract

For a graph $G$, let $\tau (G)$ be the maximum number of colors such that there exists an edge-coloring of $G$ with no two color classes being isomorphic. We investigate the behavior of $\tau (G)$ when $G=G(n,p)$ is the classical Erdős-Rényi random graph.