Totally Multicoloured Cycles

Let h(p, n) be the minimum integer such that for every edge-colouring of the complete graph of order n which uses exactly h(n,p) colours, there is at least one cycle of length p all whose edges have different colours. We prove that for every n ≤ p ≤ 3 + re(n,p−1)P2 − re(n,p − 1) + 1)2 ≤ h(n,p) ≤ f(n,p) = np − 1 p − 12 + np − 1 + re(n,p − 1)2 − 1) is the residue of n mod (p-1).