An anti-Ramsey condition on trees (Q1010730)

Summary: Let \(H\) be a finite tree. We consider trees \(T\) such that if the edges of \(T\) are colored so that no color occurs more than \(b\) times, then \(T\) has a subgraph isomorphic to \(H\) in which no color is repeated. We will show that if \(H\) falls into a few classes of trees, including those of diameter at most 4, then the minimum value of \(e(T)\) is provided by a known construction, supporting a conjecture of Bohman, Frieze, Pikhurko and Smyth.