A new construction of non-extendable intersecting families of sets

Article Type

Research Article

Publication Title

Electronic Journal of Combinatorics

Abstract

In 1975, Lovász conjectured that any maximal intersecting family of k-sets has at most (Formula Presented) blocks, where e is the base of the natural logarithm. This conjecture was disproved in 1996 by Frankl and his co-authors. In this short note, we reprove the result of Frankl et al. using a vastly simplified construction of maximal intersecting families with many blocks. This construction yields a maximal intersecting family Gk of k-sets whose number of blocks is asymptotic to e2(Formula Presented) as k → ∞.

DOI

10.37236/5976

Publication Date

8-19-2016

Comments

Open Access; Gold Open Access

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