On the Number of Minimal Separators in Graphs

We consider the largest number of minimal separators a graph on n vertices can have at most. We give a new proof that this number is in O( ((1+√5)/2)n n ). We prove that this number is in ω( 1.4521n ), improving on the previous best lower bound of Omega(3n/3) subseteq 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.