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An Anti-Ramsey Theorem on Cycles

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Abstract

Let h(n,p) be the minimum integer such that every edge-colouring of the complete graph of order n, using exactly h(n,p) colours, produces at least one cycle of order p having all its edges of different colours. In this paper the value of h(n,p) is determinated for n≥p≥3. As a corollary we obtain the equality which was conjectured by Erdös, Simonovits and Sós, 30 years ago [4].

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Authors and Affiliations

  1. Instituto de Matemáticas, UNAM, Circuito Exterior, Cd. Universitaria, México, 04510, D.F, México

    J.J. Montellano-Ballesteros

  2. Instituto de Matemáticas, UNAM, Circuito Exterior, Cd. Universitaria, México, 04510, D.F, México

    V. Neumann-Lara

Authors
  1. J.J. Montellano-Ballesteros
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  2. V. Neumann-Lara
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Correspondence to J.J. Montellano-Ballesteros.

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Received: April, 2003

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Montellano-Ballesteros, J., Neumann-Lara, V. An Anti-Ramsey Theorem on Cycles. Graphs and Combinatorics 21, 343–354 (2005). https://doi.org/10.1007/s00373-005-0619-y

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  • DOI: https://doi.org/10.1007/s00373-005-0619-y

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