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On rainbow cycles in edge colored complete graphs

Akbari, S ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. Publisher: 2007
  3. Abstract:
  4. In this paper we consider optimal edge colored complete graphs. We show that in any optimal edge coloring of the complete graph Kn, there is a Hamilton cycle with at most √8n different colors. We also prove that in every proper edge coloring of the complete graph Kn, there is a rainbow cycle with at least n/2 - 1 colors (A rainbow cycle is a cycle whose all edges have different colors). We show that for sufficiently large n, the expected number of different colors appearing on a random Hamilton cycle is approximately (1 - e-1)n for any optimal edge coloring of Kn. Finally it is proved that if Kn is colored using an abelian group of odd order n, then it has a rainbow Hamilton cycle
  5. Keywords:
  7. Source: Australasian Journal of Combinatorics ; Volume 37 , 2007 , Pages 33-42 ; 10344942 (ISSN)
  8. URL: http://ajc.maths.uq.edu.au/pdf/37/ajc_v37_p033.pdf