Multiply balanced edge colorings of multigraphs
Journal of Graph Theory
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For m ≥ 1 and p ≥ 2, given a set of integers s1,…,sq with $s_j \geq p+1$ for $1 \leq j \leq q$ and ${\sum _{j\,=\,1}^q} s_j = mp$, necessary and sufficient conditions are found for the existence of a hamilton decomposition of the complete p-partite graph $K_{m,\ldots,m} - E(U)$, where U is a 2-factor of $K_{m,\ldots,m}$ consisting of q cycles, the jth cycle having length sj. This result is then used to completely solve the problem when p = 3, removing the condition that $s_j\ge p+1$. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 208–214, 2003