A family of subsets of an n-set is 4-locally thin if for every quadruple of its members the ground set has at least one element contained in exactly 1 of them. We show that such a family has at most 20.4561n members. This improves on our previous results with Noga Alon. The new proof is based on a more careful analysis of the self-similarity of the graph associated with such set families by the graph entropy bounding technique. © 2001 Academic Press.
A Better Bound for Locally Thin Set Families / Fachini, Emanuela; Korner, Janos; Monti, Angelo. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - STAMPA. - 95:2(2001), pp. 209-218. [10.1006/jcta.2000.3162]
A Better Bound for Locally Thin Set Families
FACHINI, Emanuela;KORNER, JANOS;MONTI, Angelo
2001
Abstract
A family of subsets of an n-set is 4-locally thin if for every quadruple of its members the ground set has at least one element contained in exactly 1 of them. We show that such a family has at most 20.4561n members. This improves on our previous results with Noga Alon. The new proof is based on a more careful analysis of the self-similarity of the graph associated with such set families by the graph entropy bounding technique. © 2001 Academic Press.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
