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{\bf Petteri Kaski and Patric R. J. \"Osterg\aa rd}
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{\bf One-Factorizations of Regular Graphs of Order 12}
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Algorithms for classifying one-factorizations of regular graphs are
studied.  The smallest open case is currently graphs of order 12;
one-factorizations of $r$-regular graphs of order 12 are here
classified for $r\leq 6$ and $r=10,11$.  Two different approaches are
used for regular graphs of small degree; these proceed one-factor by
one-factor and vertex by vertex, respectively. For degree $r=11$, we
have one-factorizations of $K_{12}$. These have earlier been
classified, but a new approach is presented which views these as
certain triple systems on $4n-1$ points and utilizes an approach
developed for classifying Steiner triple systems.  Some properties of
the classified one-factorizations are also tabulated.  

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