Title: Edge colouring
Abstract: An edge-colouring of a graph is an assignment of colours to its edges so that no two edges incident with the same vertex receive the same colour; the minimum number of needed colours is called the chromatic index of and is denoted by .
A celebrated theorem of Vizing (1964) states that, for a simple graph
In 1985, Chetwynd and Hilton made the following conjecture:
We shall prove this conjecture for some special case.