Vizing's theorem

In graph theory, '''Vizing's theorem''' states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than the maximum degree of the graph. At least colors are always necessary, so the undirected graphs may be partitioned into two classes: "class one" graphs for which colors suffice, and "class two" graphs for which colors are necessary. A more general version of Vizing's theorem states that every undirected multigraph without loops can be colored with at most colors, where is the multiplicity of the multigraph. The theorem is named for Vadim G. Vizing who published it in 1964. Provided by Wikipedia