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The density of a maximum minimal cut in the subset lattice of a finite set is almost one. (English) Zbl 0787.05059

Summary: Let \(G_ n\) be a Hasse diagram of the subset lattice of a set with \(n\) elements. It is shown that, for any \(\delta>0\), there is a minimal cut of \(G_ n\) which has more than \((1-\delta)2^ n\) elements whenever \(n\) is large enough, and that the density of a maximum minimal cut of \(G_ n\) is 1/2 when \(n\leq 5\), where 5 is best possible.

MSC:

05C35 Extremal problems in graph theory
05C38 Paths and cycles
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References:

[1] Shi, F., Minimal cuts in the lattice of subsets, J. Changsha Railway Institute, 8 (1990)
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