Uwe Leck, Volker Leck
There is no ODC with all pages isomorphic to $C_4 \,\dot{\cup}\, C_3 \,\dot{\cup}\, C_3 \,\dot{\cup}\, v$
Preprint series: Preprints aus dem Fachbereich Mathematik, Unive rsität Rostock
05B30 Other designs, configurations, See also {51E30}
05B15 Orthogonal arrays, Latin squares, Room squares
Abstract: Let $n$ be a natural number and ${\cal C} = \{P_0,\dots ,P_{n-1}\}$
a collection of spanning subgraphs of $K_n$, the
complete graph on $n$ vertices.
$\cal C$ is called an Orthogonal Double Cover (ODC) if every edge of
$K_n$ belongs to exactly two elements of $\,\cal C$ and every two
elements of $\cal C$ have exactly one edge in common. Gronau, Mullin
and Schellenberg showed that the complete graph $K_n$ has an ODC
whose elements consist of cycles of length at most $4$ and an
isolated vertex, except for finitely many $n$. In this paper we
scetch the computer aided proof of the nonexistence of such an ODC
for $n=11$.
Keywords: Orthogonal Double Cover