Orthogonal double covers of complete graphs by trees of small diameter

Abstract

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 four vertices admits an ODC of the fitting K n . 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.