Locally Thin Set Families

Authors:
Noga Alon;Emanuela Fachini;János Körner
Affiliations:
Department of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel (e-mail: noga@math.tau.ac.il);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);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)
Venue:
Combinatorics, Probability and Computing
Year:
2000

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Abstract

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.