Orthogonal double covers of complete graphs by trees of small diameter Original Research Article

A collection P of n spanning subgraphs of the complete graph Kn is an orthogonal double cover (ODC) of Kn if every edge of Kn belongs to exactly two members of P, and if every two members of P share exactly one edge. P is an ODC of Kn 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 four vertices admits an ODC of the fitting Kn. They proved this to be true for trees of diameter 3. In this paper, we show the correctness of their conjecture for some classes of trees of diameter 4.