Let G be a simple undirected graph on n vertices with maximum degree ∆. Brooks’ Theorem states that G has a ∆-colouring unless G is a complete graph, or a cycle with an odd number of vertices. To recolour G is to obtain a new proper colouring by changing the colour of one vertex. We show an analogue of Brooks’ Theorem by proving that from any k-colouring, k > ∆, a ∆-colouring of G can be obtain...
