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 .
• – We prove that this number is in , improving on the previous best lower bound of .

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.