A new construction of non-extendable intersecting families of sets

In 1975, Lovasz conjectured that any maximal intersecting family of k-sets has at most [(e - 1)k!] 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 G(k) of k-sets whose number of blocks is asymptotic to e(2)(k/2)(k-1) as k -> infinity.