1 INTRODUCTION Let F $F$ and G $G$ be graphs. We say that an edge-coloring of G $G$ contains a rainbow F $F$ if G $G$ contains a subgraph isomorphic to F $F$ such that all edges are assigned distinct colors. The existence of a rainbow F $F$ in a ground graph G $G$ could be forced by simply using a lot of colors, by requiring that each vertex of G $G$ is incident to sufficiently many colors, or by making sure that each vertex of G $G$ is not incident to too many edges of the same color.
