A Quantitative Approach to Perfect One-Factorizations of Complete Bipartite Graphs
Keyword(s):
Given a one-factorization $\mathcal{F}$ of the complete bipartite graph $K_{n,n}$, let ${\sf pf}(\mathcal{F})$ denote the number of Hamiltonian cycles obtained by taking pairwise unions of perfect matchings in $\mathcal{F}$. Let ${\sf pf}(n)$ be the maximum of ${\sf pf}(\mathcal{F})$ over all one-factorizations $\mathcal{F}$ of $K_{n,n}$. In this work we prove that ${\sf pf}(n)\geq n^2/4$, for all $n\geq 2$.
2013 ◽
Vol 22
(5)
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pp. 783-799
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Keyword(s):
1968 ◽
Vol 11
(5)
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pp. 729-732
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2013 ◽
Vol 3
(3)
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pp. 390-396
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Keyword(s):
2015 ◽
pp. 55-58
2021 ◽
Vol 12
(2)
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pp. 1040-1046