Orthogonal double covers of general graphs Original Research Article

Let H be a graph on n vertices and image a collection of n subgraphs of H, one for each vertex. Then image is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of image and any two members share an edge whenever the corresponding vertices are adjacent in H. ODCs of complete graphs have been widely studied in literature. In this paper we are concerned with ODCs of arbitrary graphs. In particular, we investigate the existence of ODCs whose members are isomorphic sets of independent edges.