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Bonferroni-Type Inequalities via Chordal Graphs

Published online by Cambridge University Press:  06 September 2002

KLAUS DOHMEN
KLAUS DOHMEN
Affiliation:
Department of Informatics, Federal Armed Forces University Munich, 85577 Neubiberg, Germany (e-mail: dohmen@informatik.unibw-muenchen.de)
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Abstract

Let {Av}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.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 11 , Issue 4 , July 2002 , pp. 349 - 351
Copyright
2002 Cambridge University Press

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