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Balanced path decomposition of $λ K_{n, n}$ and $λ K_{n, n}^{*}$

Hung-Chih Lee; Chiang Lin — 2009

Czechoslovak Mathematical Journal

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

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Balanced path decomposition of λ K n , n and λ K n , n *

Balanced path decomposition of $λ K_{n, n}$ and $λ K_{n, n}^{*}$