Bonferroni-Type Inequalities via Chordal Graphs

Source abstract

Let { A v } v ∈ V be a finite collection of events and G = ( V , E ) be a chordal graph. Our main result – the chordal graph sieve – is a Bonferroni-type inequality where the selection of intersections in the estimates is determined by a chordal graph G . It interpolates between Boole's inequality ( G empty) and the sieve formula ( G complete). By varying G , several inequalities both well-known and new are obtained in a concise and unified way.