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On decomposing complete tripartite graphs into 5-cycles

Alipour, S ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. Publisher: AJC , 2012
  3. Abstract:
  4. The problem of finding necessary and sufficient conditions to decompose a complete tripartite graph K(r, s, t) into 5-cycles was first considered by Mahmoodian and Mirzakhani (1995). They stated some necessary conditions and conjectured that these conditions are also sufficient. Since then, many cases of the problem have been solved by various authors; however the case when the partite sets r ≤ s ≤ t have odd and distinct sizes remains open. A necessary condition is t ≤ 3r. Billington and Cavenagh (2011) have shown that when r, s, and t are all odd and r ≤ s ≤ t ≤ κr, where κ ≈ 1.0806, then the conjectured necessary conditions for decomposing are also sufficient. We extend this result further to the cases where κ ≈ 5/3
  5. Keywords:
  6. Tripartite graphs ; Partite sets
  7. Source: Australasian Journal of Combinatorics ; Volume 54, Issue 2 , 2012 , Pages 289-301 ; 10344942 (ISSN)
  8. URL: ajc.maths.uq.edu.au/pdf/54/ajc_v54_p289.pdf