2 research outputs found
Reconstruction of Random Colourings
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 -colourings on the -ary tree for
large . Bhatnagar et. al. showed non-reconstruction when and reconstruction when . We tighten this result and show non-reconstruction when and reconstruction when .Comment: Added references, updated notatio
5-Regular graphs are 3-colorable with positive probability
Abstract. We show that uniformly random 5-regular graphs of n vertices are 3-colorable with probability that is positive independently of n.