A note on cyclic m-cycle systems of K r(m)

Shung Liang Wu*, Hung-Lin Fu

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

It was proved by Buratti and Del Fra that for each pair of odd integers r and m, there exists a cyclic m-cycle system of the balanced complete r-partite graph K r(m) except for the case when r=m=3. In this note, we study the existence of a cyclic m-cycle system of K r(m) where r or m is even. Combining the work of Buratti and Del Fra, we prove that cyclic m-cycle systems of K r(m) exist if and only if (a) K r(m) is an even graph (b) (r, m) ≠ (3, 3) and (c) (r,m) ≢ (t , 2) (mod 4) where t ∈ {2,3}.

Original languageEnglish
Pages (from-to)427-432
Number of pages6
JournalGraphs and Combinatorics
Volume22
Issue number3
DOIs
StatePublished - 1 Nov 2006

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