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A collection P of n spanning subgraphs of the complete graph K n is an orthogonal double cover (ODC) of K n if every edge of K n belongs to exactly two members of P, and if every two members of P share exactly one edge. P is an ODC of K n by some graph G if all graphs in P are isomorphic to G. Gronau, Mullin, and Rosa conjecture that every tree except the path with...
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