A properly edge-colored graph is a graph with a coloring of its edges such that no vertex is incident to two or more edges of the same color. A subgraph is called rainbow if all its edges have different colors. The problem of finding rainbow subgraphs or other restricted structures in edge-colored graphs has a long history, dating back to Euler's work on Latin squares. It has also proven to be a powerful method for studying several well-known questions in other areas. In this survey, we will provide a brief introduction to this topic, discuss several results in this area, and demonstrate their applications to problems in graph decomposition, additive combinatorics, theoretical computer science, and coding theory.

翻译：恰当边着色图是指对其边进行着色，使得任意顶点不关联两条或更多同色边的图。若子图的所有边颜色互不相同，则称该子图为彩虹子图。在边着色图中寻找彩虹子图或其他受限结构的问题具有悠久历史，可追溯至欧拉关于拉丁方的研究。该方法亦被证明是研究其他领域中若干经典问题的有力工具。本综述将简要介绍该主题，讨论该领域的若干结果，并展示其在图分解、加性组合学、理论计算机科学和编码理论问题中的应用。