A survey on star edge-coloring of graphs

Abstract: The star chromatic index of a multigraph $G$, denoted $\chi'_{st}(G)$, is the minimum number of colors needed to properly color the edges of $G$ such that no path or cycle of length four is bicolored. We survey the results of determining the star chromatic index, present the interesting proofs and techniques, and collect many open problems and conjectures.