On the Anti-Ramsey Threshold for Non-Balanced Graphs

For graphs G, H, we write G rb H if for every proper edge-coloring of G there is a rainbow copy of H, i. e. , a copy where no color appears more than once. Kohayakawa, Konstadinidis and the last author proved that the threshold for G (n, p) rb H is at most n^-1/m₂ (H). Previous results have matched the lower bound for this anti-Ramsey threshold for cycles and complete graphs with at least 5 vertices. Kohayakawa, Konstadinidis and the last author also presented an infinite family of graphs H for which the anti-Ramsey threshold is asymptotically smaller than n^-1/m₂ (H). In this paper, we devise a framework that provides a richer family of such graphs.