Edge coloring is a concept in graph theory where the edges of a graph are assigned colors in such a way that no two adjacent edges share the same color. This is important for various applications, such as scheduling problems and network design, where conflicts must be avoided. The goal of edge coloring is to use the minimum number of colors possible, known as the chromatic index. A well-known theorem related to edge coloring is Vizing's theorem, which states that the chromatic index of a simple graph is either equal to its maximum degree or one more than that.