A note on the four-colourability of pedigrees and its consequences for probability calculations

A graph representing the probabilistic dependences between genotypes of individuals in a pedigree is shown to be four-colourable. The consequences of this for computation of probabilities, using both exact and Markov chain Monte Carlo methods, is discussed. A four-colouring and triangulation of an inbred section of a pedigree of Red-Crowned Cranes is illustrated.