Reconstruction problems have been studied in a number of contexts including
biology, information theory and and statistical physics. We consider the
reconstruction problem for random k-colourings on the Δ-ary tree for
large k. Bhatnagar et. al. showed non-reconstruction when Δ≤21klogk−o(klogk) and reconstruction when Δ≥klogk+o(klogk). We tighten this result and show non-reconstruction when Δ≤k[logk+loglogk+1−ln2−o(1)] and reconstruction when Δ≥k[logk+loglogk+1+o(1)].Comment: Added references, updated notatio