Geodesic
One-factorizations of regular graphs of order 12
The electronic journal of combinatorics, Tome 12 (2005)
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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.
DOI : 10.37236/1899
Classification : 05C70, 05-04, 05C85
Mots-clés : triple system, algorithms 
@article{10_37236_1899,
     author = {Petteri Kaski and Patric R. J. \"Osterg\r{a}rd},
     title = {One-factorizations of regular graphs of order 12},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1899},
     zbl = {1062.05120},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1899/}
}
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Petteri Kaski; Patric R. J. Östergård. One-factorizations of regular graphs of order 12. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1899

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