Intersection theorems on structures

Miklós Simonovits, Vera T. Sós

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This chapter describes intersection theorems on graphs and integers. The most elementary intersection theorems are the ones on sets. In these cases a set S has been fixed and a family A = {Al, …, AN} of subsets of S, assumes that the sets A1, …, AN have some intersection property P. Then it has been asked that for the maximum N in terms of ISI or other parameters, specified in P. More generally instead of an intersection property one can consider any Boole-algebraic property, involving intersection, union, disjointness, complement, containment, rank or size, and ask for maximal or minimal sized families of subsets satisfying the given conditions.

Original languageEnglish
Pages (from-to)301-313
Number of pages13
JournalAnnals of Discrete Mathematics
Issue numberC
Publication statusPublished - Jan 1 1980


ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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