Let \(\) be the Turán number which gives the maximum size of a graph of order \(\) containing no subgraph isomorphic to \(\).
In 1973, Erdős, Simonovits and Sós  proved the existence of an integer \(\) such that for every integer \(\), the minimum number of colours \(\), such that every \(\)-colouring of the edges of \(\) which uses all the colours produces at least one \(\) all whose edges have different colours, is given by \(\). However, no estimation of \(\) was given in . In this paper we prove that \(\) for \(\). This formula covers all the relevant values of n and p.
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