An Anti-Ramsey Theorem

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 [5] 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 [5]. In this paper we prove that for . This formula covers all the relevant values of n and p.

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Received January 27, 1997/Revised March 14, 2000

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Montellano-Ballesteros, J., Neumann-Lara, V. An Anti-Ramsey Theorem. Combinatorica 22, 445–449 (2002). https://doi.org/10.1007/s004930200023

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  • AMS Subject Classification (1991) Classes:  05C35, 05C99