Recent progress on edge-colouring graphs

In this note, multigraphs will have no loops. For a multigraph G, the least number of colours needed to colour the edges of G in such a way that no two edges on the same vertex of G have the same colour, is called the edge-chromatic number, or the chromatic index, of G. It is clear that if A(G) denotes the chromatic index of G, then A(G) <x'(G). If A(G) = x ' (G) , then G is said to be Class 1, and otherwise G is Class 2. If G is a simple graph, then Vizing [17] showed that x ' (G) ~< A(G) + 1. If