Abstract
Consider a graph G with a one-factorization F = {F l, F 2, ...}. Suppose H is a subgraph of G. Normally H ⋂ F i will consist of some edges and some vertices. It may be, however, that for every i, H ⋂ F i consists either only of edges or only of vertices; in other words each H ⋂ F i either is a one-factor of H or has edge-set ∅. If this occurs, order the F i so that H ⋂ F 1, H ⋂ F 2, ..., H ⋂ F t are one-factors in H, while H ⋂ F j has no edges for j > t. Then the first t factors H ⋂ F j form a one-factorization of H, and this is called a subfactorization of.F (or a subfactorization of H in G).
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© 1997 Springer Science+Business Media Dordrecht
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Wallis, W.D. (1997). Subfactorizations and Asymptotic Numbers of One-Factorizations. In: One-Factorizations. Mathematics and Its Applications, vol 390. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2564-3_14
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DOI: https://doi.org/10.1007/978-1-4757-2564-3_14
Publisher Name: Springer, Boston, MA
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