Randomly Colouring Sparse Random Graphs using a Constant number of colours

In this work we present an efficient algorithm which, with high probability, provides an almost uniform sample from the set of proper χ-colourings of an instance of sparse random graphs Gn,d/n, where χ = χ(d) is a sufficiently large constant. This work improves, asymptotically, the result of Dyer, Flaxman Frieze and Vigoda in (4) where the algorithm proposed there needs at least �( log log n