Abstract
Publisher Summary 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 = {A l , . . . , A N } of subsets of S, assumes that the sets A 1 , . . . , A N 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.
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