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Combinatorica

, Volume 22, Issue 3, pp 445–449 | Cite as

An Anti-Ramsey Theorem

  • J. J. Montellano-Ballesteros
  • V. Neumann-Lara
Original Paper

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.

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

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Copyright information

© János Bolyai Mathematical Society, 2002

Authors and Affiliations

  • J. J. Montellano-Ballesteros
    • 1
  • V. Neumann-Lara
    • 2
  1. 1.Instituto de Matemáticas, UNAM; Circuito Exterior, Ciudad Universitaria, México 04510, D. F., México; E-mail: juancho@math.unam.mxMX
  2. 2.Instituto de Matemáticas, UNAM; Circuito Exterior, Ciudad Universitaria, México 04510, D. F., México; E-mail: neumann@math.unam.mxMX

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