10.18453/rosdok_id00005900 Froncek, Dalibor Dalibor Froncek http://d-nb.info/gnd/130012319 https://orcid.org/0000-0003-4528-2059 Leck, Uwe Uwe Leck http://d-nb.info/gnd/123092418 University of Rostock, Institute of Mathematics 2005 510 Mathematics 2005 en https://purl.uni-rostock.de/rosdok/id00005900 urn:nbn:de:gbv:28-rosdok_id00005900-7 An orthogonal double cover (ODC) of the complete graph Kn by some graph G is a collection of n spanning subgraphs of Kn, all isomorphic to G, such that any two of the subgraphs share exactly one edge and every Edge of Kn is contained in exactly two of the subgraphs. A necessary condition for such an ODC to exist is that G has exactly n-1 edges. We show that for any given positive integer d, almost all caterpillars of diameter d admit an ODC of the corresponding complete graph.