A conjecture in extremal combinatorics

An independence system is a family of sets closed under taking subsets: if I is an independence system, if T belongs to I, and if S is a subset of T, then S also belongs to I. An intersecting family is a family of sets that includes no two disjoint sets. A star in an independence system consists of all its members that include a prescribed point. The independence system that consists only of the empty set is an intersecting family and it has no nonempty star. The conjecture (Problem 25) in The following papers are directly related to this conjecture:

A conjecture in extremal combinatorics A conjecture in extremal combinatorics An independence system is a family of sets closed under taking subsets: if I is an independence system, if T belongs to I , and if S is a subset of T , then S also belongs to I . An intersecting family is a family of sets that includes no two disjoint sets. A star in an independence system consists of all its members that include a prescribed point. The independence system that consists only of the empty set is an intersecting family and it has no nonempty star. The conjecture (Problem 25) in Selected combinatorial r

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