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Locally Thin Set Families

Published online by Cambridge University Press:  09 April 2001

NOGA ALON ,
EMANUELA FACHINI  and
JÁNOS KÖRNER
NOGA ALON
Affiliation:
Department of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel (e-mail: noga@math.tau.ac.il)
EMANUELA FACHINI
Affiliation:
Department of Computer Science, University of Rome I ‘La Sapienza’, Via Salaria 113, 00198 Roma, Italy (e-mail: fachini@dsi.uniroma1.it, korner@dsi.uniroma1.it)
JÁNOS KÖRNER
Affiliation:
Department of Computer Science, University of Rome I ‘La Sapienza’, Via Salaria 113, 00198 Roma, Italy (e-mail: fachini@dsi.uniroma1.it, korner@dsi.uniroma1.it)
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Abstract

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A family of subsets of an n-set is k-locally thin if, for every k of its member sets, the ground set has at least one element contained in exactly 1 of them. We derive new asymptotic upper bounds for the maximum cardinality of locally thin set families for every even k. This improves on previous results of two of the authors with Monti.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 9 , Issue 6 , November 2000 , pp. 481 - 488
Copyright
2000 Cambridge University Press