**MSC:**- 05A05 Combinatorial choice problems (subsets, representatives, permutations)

$K_n$

is called an {\cal orthogonal double cover} if (i) every edge of $K_n$

belongs to exactly two of the $G_i$'s and (ii) any two distinct $G_i$'s

intersect in exactly one edge. Chung and West conjectured that there

exists an orthogonal double cover of $K_n$ for all $n$, in wich each

$G_i$ has maximum degree 2, and proved this result for $n$ in six of

the residue classes modulo 12. In anover context, Ganter and Gronau

showed that for $n\equiv 1 \mbox{ mod } 3$, $n \not=10$, there exists

an orthogonal double cover of $K_n$ in wich each $G_i$ consists of an

isolated vertex and the vertex disjoint union of $K_3$'s (actually

these orthogonal double covers result from the solution of the

directed version of the problem, wich reduces to the undirected case

when the orientation of the arcs is ignored). Clearly the covers of

Ganter and Gronau satisfy the Chung-West requirement. In this paper,

the configurations of Ganter and Gronau are generalized to include the

cases $n \equiv 0,2 \mbox{ mod } 3$, and the results are used to

provide a

unified solution of the Chung-West problem.

For $n\not\equiv 5\mbox{ mod } 6$, all the spanning subgraphs in the

collection

${\cal G}$ are isomorphic to each other; however, this is not the case

when $n\not\equiv 5\mbox{ mod } 6$. In addition to solving the

Chung-West

problem, we also go on to show that for $n\equiv 2\mbox{ mod } 3$,

and $n>287$,

there exists an orthogonal double cover of $K_n$ in wich each spanning

subgraph $G_i$ consists of the vertex-disjoint union of an isolated

vertex, a quadrilateral, and $(n-5)/3$ triangels. Of the 96 cases with

$2\leq n \leq 287, 65$ cases are resolved and 31 remain open.