Class two regular graph
= Class two regular graph
An $r$-<regular graph> is class two when its <edge chromatic number> exceeds $r$. For a finite <simple graph>, <Vizing's theorem> makes that <edge chromatic number> exactly $r+1$. An $r$-colour <proper edge colouring> of an $r$-<regular graph> would partition its <edges> into $r$ <perfect matchings>, since every <vertex> would see each colour exactly once.