Multicolour Ramsey numbers of odd cycles

We show that for any positive integer r there exists an integer k and a k-colouring of the edges of K2k+1 with no monochromatic odd cycle of length less than r. This makes progress on a problem of Erdős and Graham and answers a question of Chung. We use these colourings to give new lower bounds on the k-colour Ramsey number of the odd cycle and prove that, for all odd r and all k sufficiently large, there exists a constant ϵ=ϵ(r)>0 such that Rk(Cr)>(r−1)(2+ϵ)k−1.