Edge-Colorings of Complete Bipartite Graphs Without Large Rainbow Trees

Abstract

Let $\mathcal{G}$ be a family of graphs. The anti-Ramsey number $\text{AR}(n,\mathcal{G})$ for $\mathcal{G}$ is the maximum number
of colors in an edge coloring of $K_n$ that has no rainbow copy of
any graph in $\mathcal{G}$. In this paper, we determine the bipartite anti-Ramsey number for the family of trees with
$k$ edges.