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Keywords:
cycles; decomposing complete tripartite graphs
Summary:
The complete tripartite graph $K_{n,n,n}$ has $3n^2$ edges. For any collection of positive integers $x_1,x_2,\dots ,x_m$ with $\sum _{i=1}^m x_i=3n^2$ and $x_i\ge 3$ for $1\le i\le m$, we exhibit an edge-disjoint decomposition of $K_{n,n,n}$ into closed trails (circuits) of lengths $x_1,x_2,\dots ,x_m$.
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