Abstract
One-factors of the complete graph K2r on 2r vertices are considered. A set S of less than 2r-1 of these one-factors is called maximal if they are pairwise edge-disjoint, and if there is no one-factor of K2r which is edge-disjoint from all members of S.
It is shown that a maximal set in K2r must contain at least r one-factors, and that if r is even then the smallest possible maximal set has r+1 members; and both of these bounds can be realized. In fact, if n is odd and n ≤ r, then K2r contains a maximal set of 2r-n one-factors.
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References
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© 1975 Springer-Verlag
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Cousins, E., Wallis, W.D. (1975). Maximal sets of one-factors. In: Street, A.P., Wallis, W.D. (eds) Combinatorial Mathematics III. Lecture Notes in Mathematics, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069547
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DOI: https://doi.org/10.1007/BFb0069547
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