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path decomposition; balanced decomposition; complete bipartite graph
Let $P_k$ denote a path with $k$ edges and $łK_{n,n}$ denote the $ł$-fold complete bipartite graph with both parts of size $n$. In this paper, we obtain the necessary and sufficient conditions for $łK_{n,n}$ to have a balanced $P_k$-decomposition. We also obtain the directed version of this result.
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