A note on uniform intersecting families with maximum transversal size

Abstract

We construct an intersecting $k$-family of transversal size $\lceil \frac{k+1}{2}\rceil$ and length $k+1$ and study some of its properties. We use this family to prove that $q(4)=9$. We also construct a $k$-family for $k=2^m-1$ of length $2k+1$ and transversal size at least $(2k+1)/3$.

5 pages