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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

THE MAXIMUM SIZE OF A NON-TRIVIAL INTERSECTING UNIFORM FAMILY THAT IS NOT A SUBFAMILY OF THE HILTON-MILNER FAMILY

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Author(s):
Han, Jie ; Kohayakawa, Yoshiharu
Total Authors: 2
Document type: Journal article
Source: Proceedings of the American Mathematical Society; v. 145, n. 1, p. 73-87, JAN 2017.
Web of Science Citations: 4
Abstract

The celebrated Erdos-Ko-Rado theorem determines the maximum size of a k-uniform intersecting family. The Hilton-Milner theorem determines the maximum size of a k-uniform intersecting family that is not a subfamily of the so-called Erdos-Ko-Rado family. In turn, it is natural to ask what the maximum size of an intersecting k-uniform family that is neither a subfamily of the Erdos-Ko-Rado family nor of the Hilton-Milner family is. For k >= 4, this was solved (implicitly) in the same paper by Hilton-Milner in 1967. We give a different and simpler proof, based on the shifting method, which allows us to solve all cases k >= 3 and characterize all extremal families achieving the extremal value. (AU)

FAPESP's process: 15/07869-8 - Perfect matchings and Tilings in hypergraphs
Grantee:Jie Han
Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
FAPESP's process: 14/18641-5 - Hamilton cycles and tiling problems in hypergraphs
Grantee:Jie Han
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
Grantee:Oswaldo Baffa Filho
Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
FAPESP's process: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science
Grantee:Carlos Eduardo Ferreira
Support Opportunities: Research Projects - Thematic Grants