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Orthogonal double covers of general graphs. (English) Zbl 1034.05040
Summary: Let $H$ be a graph on $n$ vertices and $𝒢$ a collection of $n$ subgraphs of $H$, one for each vertex. Then $𝒢$ is an orthogonal double cover (ODC) of $H$ if every edge of $H$ occurs in exactly two members of $𝒢$ and any two members share an edge whenever the corresponding vertices are adjacent in $H$. ODCs of complete graphs have been widely studied in the 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.
##### MSC:
 05C70 Factorization, etc.
##### Keywords:
Edge decomposition; Factorization; ODC; Regular graph; Hypercube