Covers in uniform intersecting families and a counterexample to a conjecture of Lovász

Abstract

We discuss the maximum size of uniform intersecting families with covering number at least τ. Among others, we construct a large k-uniform intersecting family with covering number k, which provides a counterexample to a conjecture of Lovász. The construction for odd k can be visualized on an annulus, while for even k on a Möbius band. © 1996 Academic Press, Inc.