One-factorizations of regular graphs of order 12

Reference:

Petteri Kaski and Patric R. J. Östergård. One-factorizations of regular graphs of order 12. Electronic Journal of Combinatorics, 12:R2, 2005.

Abstract:

Algorithms for classifying one-factorizations of regular graphs are studied. The smallest open case is currently graphs of order 12; one-factorizations of -regular graphs of order 12 are here classified for and . 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 , we have one-factorizations of . These have earlier been classified, but a new approach is presented which views these as certain triple systems on points and utilizes an approach developed for classifying Steiner triple systems. Some properties of the classified one-factorizations are also tabulated.

Suggested BibTeX entry:

@article{KaOs05,
    author = {Petteri Kaski and Patric R. J. {\"O}sterg{\aa}rd},
    journal = {Electronic Journal of Combinatorics},
    pages = {R2},
    title = {One-factorizations of regular graphs of order 12},
    volume = {12},
    year = {2005},
}