Geodesic
Decomposing complete tripartite graphs into closed trails of arbitrary lengths
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 523-551 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $x_1,x_2,\dots ,x_m$.
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 $x_1,x_2,\dots ,x_m$.
Classification : 05C38, 05C70
Keywords: cycles; decomposing complete tripartite graphs 
@article{CMJ_2007_57_2_a1,
     author = {Billington, Elizabeth J. and Cavenagh, Nicholas J.},
     title = {Decomposing complete tripartite graphs into closed trails of arbitrary lengths},
     journal = {Czechoslovak Mathematical Journal},
     pages = {523--551},
     year = {2007},
     volume = {57},
     number = {2},
     mrnumber = {2337613},
     zbl = {1174.05100},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a1/}
}
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Billington, Elizabeth J.; Cavenagh, Nicholas J. Decomposing complete tripartite graphs into closed trails of arbitrary lengths. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 523-551. http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a1/