On the number of minimal separators in graphs

Weconsider the largest number of minimal separators a graph on n vertices can have. –We give a new proof that this number is in O1+52n·n. –We prove that this number is in ω(1.4457n), improving on the previous best lower bound of Ω(3n/3)⊆ω(1.4422n). This gives also an improved lower bound on the number of potential maximal cliques in a graph. We would like to emphasize that our proofs are short, simple, and elementary.

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