Fractional clique decompositions of partite graphs

We give a minimum degree condition sufficient to ensure the existence of a fractional Kr -decomposition in a balanced r-partite graph (subject to some further simple necessary conditions). This generalizes the non-partite problem studied recently by Barber, Lo, Kühn, Osthus and the author, and the 3-partite fractional K 3-decomposition problem studied recently by Bowditch and Dukes. Combining our result with recent work by Barber, Kühn, Lo, Osthus and Taylor, this gives a minimum degree condition sufficient to ensure the existence of a (non-fractional) Kr -decomposition in a balanced r-partite graph (subject to the same simple necessary conditions).