Abstract
One-factors are called compatible if they have no common edge; a set of one-factors of G is called maximal if the factors are compatible but G contains no other one-factor compatible with them. A one-factorization is trivially a maximal set; a maximal set of fewer than d one-factors in a regular graph of degree d will be called proper. Theorem 8.3 essentially tells us that K n,n has no proper maximal set (see Theorem 18.13, below). It is natural to ask about the existence of proper maximal sets in K 2 n .
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© 1997 Springer Science+Business Media Dordrecht
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Wallis, W.D. (1997). Maximal Sets of Factors. In: One-Factorizations. Mathematics and Its Applications, vol 390. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2564-3_18
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DOI: https://doi.org/10.1007/978-1-4757-2564-3_18
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4766-6
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